HAL Id: inria-00073966
https://hal.inria.fr/inria-00073966
Submitted on 24 May 2006
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
A Fermat-Like Sequence and Primes of the Form 2h.3n+ 1
Yannick Saouter
To cite this version:
Yannick Saouter. A Fermat-Like Sequence and Primes of the Form 2h.3n+ 1. [Research Report]
RR-2728, INRIA. 1995. �inria-00073966�
ISSN 0249-6399
a p p o r t
d e r e c h e r c h e
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
A Fermat-like sequence and primes of the form
Yannick Saouter
N˚ 2728
Novembre 1995
PROGRAMME 1
,+-/..02143657-98;:<>=@?*A
BCEDGF*CIHJKJLMONQPCSRUT/VXWEL>RSWEY9CULZ\[]HCSH^_^2`L^_LZ>a@b]H4ZULZc@Lc@DGd/dfeLLZga]C9eLZULgHY@hiLWjZEklZEW>`LJKLZmcnVXZEWUCEVXb/YfeLZ
BCED>oSLWOPmBp
qH4[9[]D*CUWjc@LCEL>RET9LCIRET9Lrdslt*uGtGvwNyxjDz*LJ{b9CEL+M>|*|G}wN~Mg}[]H4FGLZ
g ]*69LCEJH4WjdlY/J{b]LCEZmH4CUL{HRS^HZEZUVRH4^WEDG[9VRV_diL^XLJLd@WIH4CUkd@Y9J{b;LCWET9LDGCEkl/LCUJHWjV_d@WUCUD9c@Y;RSL>c"WUT9LJHd]c
R^H4V_JL>c"WUT]H4W+H^_^WUT9LZULd@Y9J{b]LCUZ+H4CUL[/CUV_JLGjT/VXZ{RS^HV_JfH4Zc@V_ZE[9CUD@DL>cb@kY9^_LCjT9DiFlHgz*LH[/CUDG[;LCEWkDGdWET9L
LzGLd@WUY;H^c@V_zlV_ZEDGCUZD7WET9L9LCUJH4WdlY/J{b]LCEZ>pd{WET9V_ZfH4CUWUVRS^_LO(LOLSh9T9V_b9V_W(Hd9D*WUT9LCjZULCEVXLjT9D*ZULc@LS]d9V_WEVXD*d{V_ZfRS^_D*ZULWED+WET9L
D*d9LD(/LCUJHWdlY/J{b]LCEZmH4d]cKjT9VRUTLSh9T9V_b9V_WjZEVXJKV_^H4C[9CEDG[;LCUWEVXLZ>jjT9V_ZO[9CUD*b9^_LJjV_^_^^_L>HGcKY9ZOWUD{WET9LZULWUZD(RSDz*LCUV_d9F
RDGd9F*CUY9Ld;RSLZODGCd@Y9J{b;LCUZt*7¡ ¢£¤MH4ZjZUV_JV_^HCE^Xk/LCUJHWd@Y9J{b]LCUZj^_L>HGcWUD¥@V_LCE[9V_d9ZU¦@V§Zj[9CUD*b9^_LJ¨
©Kª@«¬U\®] G¯4°/LCEJHWg§Z(d@Y9J{b;LCUZg±9BCUV_JKLd@Y9J{b9CELZ>±9¥@V_LCE[9V_d9ZU¦@V§Z([/CUDGb/^XLJ
²³{´
µ2¶·>¸
´
µ¹º_¶»2¼½
¾À¿ÁÂSáÄÅ@ÆUÇÈGÉnÊUËÌIÍOÎ_ÌUÎÏÆUÇ@ÐÑÒÌ
Unite´ de recherche INRIA Rennes
IRISA, Campus universitaire de Beaulieu, 35042 RENNES Cedex (France) Te´le´phone : (33) 99 84 71 00 – Te´le´copie : (33) 99 84 71 71
ª9 ªLZmd/DGJ{b9CELZc@L{9LCEJH4WjZUDGd@WOY9diZUYgoSLWRS^HZEZUV*Y9LLdiWETjeLD*CUV_LcnLZd9DGJ{b9CELZ>;9LCUJH4Wj^_LZV_d@WUCEDncnY9Vc@V_WjLW
RDGd>oSLgRSWUY9CSH*Y9L{WUD*Y9ZRSLZd9DGJ{b/CULZOZUDGd@W[9CELJV_LCEZ>LWEWULHCUJHWEVXD*d{Y/WmJKDGd@WUC9eLHY9ZEZUL[]HC+ Y9^_LCGY/V(c@DGd/d]HKY9d9L
[/CUDG[/CUV>eLW9eLZUY/Cm^_LZc@V_z@V_ZULY/CUZ¨eLzGLdlWEY9L^_Z+c@LZmd/DGJ{b9CELZmc@L{/LCUJHW>Hd9ZRSLW+H4CUWUVRS^_Ld/DGY9ZceLS;d9V_ZUZUD*d9ZY9d/LH4Y9WUCEL+ZEY9V_WUL
cnDGd@W^HceLS;d9V_WUV_DGdLZUWj[/CUD9RET9Lmc@LRSL^_^_Lmc@LZ(d9D*J{b9CULZ(c@Lm/LCEJHWLW*Y9V;C9eLz`L^_LmcnLZ([/CUDG[/CUV>eLW9eLZjZUV_JV_^HV_CULZ>Lj[9CUD*b9^2`LJL
d/DGY9Z+RDGd]c@Y/VXCSHHY@hLd9ZELJ{b9^_LZ+c@LRDGY9z*LCUWEY9CULZcnLRSDGd9F*CUY9Ld]RSLZ{[;DGY9C\^XLZd9DGJ{b/CULZtG ¡ ¢+£ M{RSDGJKJLGa;c@L{JH4d9V2`LCUL
ZEV_JV_^HV_CUL^_LZjd9DGJ{b/CULZjc@L+/LCUJHWd9DGY/ZRSDGd]cnY9V_ZULHY[9CEDGb9^`LJKLmc@L¥@V_LCE[9V_d9ZU¦@V
¤®;¬Sªi x DGJ{b9CELZc@L9LCUJH4W>±@xjD*J{b9CULZj[/CULJKVXLCUZ>±9B CUDGb/^2`LJLmcnLw¥nVXLCU[9V_d9ZE¦lV
+#K (>#
/LCEJHWd@Y9J{b;LCUZHCULH{RS^HZUZEVRH^WUD*[9VROVXdL^_LJKLd@WIH4CUkd@Y9J{b]LCjWUT9LD*CUk@]/LCUJHWV_dlWECUD9c@Y]RL>ciWET9LJ H4d]cRS^HV_JL>cWUT]H4W
H4^_^WUT9LZELd@Y9J{b;LCUZH4CUL[9CEV_JLG*jT9V_ZRS^HV_J jHZc@V_ZE[9CUD@DL>cb@kY/^XLCjjT9D{FlHgz*LwH[/CUDG[;LCEWkD*dWUT9LLzGLd@WUY;H^cnVXz@V_ZUD*CUZ
D4(WUT/L/LCUJHWOdlY/J{b]LCEZ>;pdiWET9V_ZwH4CUWEVR^XLL+LSh9T9V_b9V_WHd9D*WUT9LCZELCUV_L{jT9D*ZULc@LS;d9V_WUV_DGdiV_ZRS^_DGZUL{WEDWET9L{DGd9LDj9LCEJH4W
d@Y9J{b;LCEZfH4d]c{jT9VRETLhnT/VXb/VXWÀZUV_JV_^HC[9CEDG[;LCUWEVXLZ>9jT/VXZ[9CEDGb9^_LJ jV_^_^;^XLgHGc{Y/ZjWUDWUT9LOZULWEZDRSDzGLCUV_d9F{RSDGd9F*CUY9Ld]RSLZ DGC
d@Y9J{b;LCjtG ¡ ¢m£&MHZjZEVXJKV_^H4CU^_k+/LCUJHWd@Y9J{b;LCEZj^XLgHGc{WED¥@V_LCU[/VXd/ZU¦@V§Zj[/CUDGb/^XLJ¨
À#+ >#% w imÀ
P RSLCUWSHV_d d@Y9J{b]LCmD4[9CUD*[]LCUWUV_LZHCEL¦@d9Djd D*C+9LCUJH4WdlY/J{b]LCEZ>Lc@Ld9D*WUL
¢
t ¢ £ MG jT9Ld (L{T;HgzGLWET9L
DG^_^_DjVXd/FmWET9LD*CULJ
"!ª@®; ª $#&%('*)(+,
¢.-0/1"243-65879;:<5>=?73A@BDCE79
tGFIH
PjWjWET9V_Zj[]D*V_dlWLwcnLd9DGWELKJ
¢
tGLNMf£¤MGILT]Hgz*LWET9LdiWET9LODG^_^_DjV_d9F[9CEDG[;LCUWkO
"!ª@®; ª $#&%P#RQ2B L[/VXd §ZWULZUWTSU
CV79;:<5>=?73
J
¢W-0/X243N-(587,-
+
1Y94Z[Y9E\^]K-
+
B_CV7N3T7`7Aab-0/TB_/Xcd
t
/:Ee?C>B_CV1bBf
Q
cOg J ¢ S
ih
M
1j94Z`c;kml Monqpr(s
L
th
MvuxwvyYz;{J
¢o|@}CV7N3T7"f~Zo79{[B7?/`B_CV7I1Ge?[G=N-//]Y5>=T[j\
H
LCELSLCWUT/L+CEL>HGc@LCmWEDWu_M
|
DGCWET9L+c@L]d9V_WUV_DGd Hd]cWET9L+RSD*J[9Y/WIHWEV_DGdCEY9^_LZDWUT/LK@HGRSD*b9V§ZjZEk@J{b]D*^2E DGCUL\[9CUL>RVXZEL^_kla
WET9Ld@Y9J{b]LCf V_ZH^_jHgk@Z(HFGD@D9cRUT/DGVRSLODGC
c
"!ª@®; ª $#&%P U
CV79E:I5>=T7N3
J ¢ -m/243-6587-
+
1j94Z[Y9E\^]>- +j
kml MGnpr6s
L
th
MuxwvyYz;4J
¢o|
H
jT9V_ZjWELZUWV_ZCSH[9Vc@^_k{Y9d@L>HZEVXb/^XL\b]L>RHY9ZEL+D4 WET9LLSh9[;DGd9LdlWEVH^7F*CUDjWETiDWUT/Ld@Y9J{b]LCUZJ
¢
a]b/Y9WjV_WjHZjY9ZEL>ciV_db@k
Y]RH4ZjWUD{ZUT/D WET]HWJOV_ZRSDGJK[]D*ZUV_WULGoLT]HgzGLH^_ZUD{
"!ª@®; ª $#&%U
CV79E:I5>=T7N3?/
J ¢ 1Y3T72E1Y-(3}-m/73?7\m1B-(Y7\^]2{3-(5>7
H
¥nDGJLjV_d@DGCUJHWEVXD*d+V_ZH4^XZED+¦@d9DjdD*dWUT/L+c@V_z@VXZEDGCEZjDJ
¢
"!ª@®; ª $#&%Pi)(+
-m/K1243N-(587ZY-(-m/[Y3K[
+J
¢ @B_CV7N9
MvuxwyYz];t ¢IOL
|H
jT9V_ZWET9LD*CULJ Ld]H4b9^_LZOL^_^_LCWUD{RS^HV_J V_diMg|GvG}wWUT]H4WXJ
L?
p
V_Zd9DGWjH[9CEV_JLZUV_d]RSLV_WV_ZfcnVXz@V_ZUV_b9^_Lb@k}toLT9£M*
PjWjWET9L[9CULZELd@WWUV_JLjWET9LDGd/^Xk/LCEJHW[9CEVXJKLjd@Y9J{b]LCUZj¦@d9DjdH4CULKJ
¢
aM
]
¡
#' >
pdWET9V_ZZULgRSWUV_DGd (Lc@LS]d/LHd9L ZULCEV_L£¢
¢.
*¢£&t¢{£ M{jT/VRETLSh9T9V_b9V_WEZWUT9LKZIH4JL{¦@V_d]ciD4[9CUD*[]LCUWUV_LZ{WET]HdWET9L
/LCEJHWÀdlY/J{b]LCEZ>ILT]Hgz*LwH4W;CUZUW
"!ª@®; ª $ &%('*)(+,¢
¢ -m/K1"243-(5>79E:I5>=?73?@BDCE79
oFEH
¥nVXJKV_^H4CU^Ïk(Lc@Ld9DGWEL`¤
¢>
oMf£ tYMf£&MGILT]Hgz*LWUT/Ldq
"!ª@®; ª $ &%P#U
CV7¥9E:I58=?7N3
¤ ¢ -m/243-(5>7-
+
1Y94Z¦[Y9;\] -
+
BDCE73?7§7?aY-m/?BD/c¨d
t
/:Ee?C¦BDCE1B>f
Q
c&g
¤ ¢ S
©h
M
1j94Z
c;kmª
M
nqpr(s
L
¦h
MvuxwyYz];¤
¢I|
H
DGCUL[9CEL>RSV_ZUL^Xk@a9WET9Ld@Y9J{b]LC}V_ZH^_jHgk@ZfH\FGD@D9cRUT/DGVRSLODGC
c
"!ª@®; ª $ &%P U
CV79E:I5>=T7N3
¤ ¢ -m/X2{3-(5>7-
+
1j94Zv[j9E\]- +j}
kmª MYnpr(s
L
¦h
MvuxwvyYz;E¤
¢I|
H
LOT]HgzGLH4^XZED4
"!ª@®; ª $ &%U
CV79E:I5>=T7N3?/
¤
¢ 1Y3T72V1j-(3}-m/73?7\m1B-(Y7\^]243-6587
H
H4d]cO
"!ª@®; ª $ &%Pi)(+
-m/K1243N-(587ZY-(-m/[Y3K[
+J
¢{@B_CV7N9
MvuxwyYz]; ¢I
p |H
pWV_ZjT9LCELd9DGWELDGCUWET@k{WUT]H4WjWUT9LLSh9[;DGd9Ld@WOVXZDGd/^Xk
£6MG@jT/LDG^_^_DjVXd/FmZEL>RSWEVXD*d9ZmH4CULc@Lz*DGWEL>cKWUD[9CUDz*LmWET9L[9CULzlV_D*Y9Z
R^H4V_JZ>
1Y9E9;-De 1o[Y:oB7N3
À##% #+%&'#+\
¡
jT/VXZ[9CEDlD4Y9ZULZOW(D^_LJJHZ
˻ %('
[j3`1Y\(\{c>d M @
tYF
MuwyYz;4¢
FN|
H
w ®®LCUVÏk{WUT;HWtYF
h M Q2toF
h
MSx¢
F
H4d]cO
˻ %P#
[j3`1Y\(\{c>d M @
tYF£ tGL?F(£&M
uwyYz;4¢
FN|
H
w ®®LCUVÏk{WUT;HWtYF£ tGL?F(£&M
Q_<F
h
toFj£6MSx¢
F
LOT]HgzGLWET9Ldq
"!ª@®; ª %('
[Y3K1j\(\Ec>d
M
1j94Z
d M @ ¢ k
S¢<
pr
F
1Y94Z
¢ k
S¢<OL
rF
1Y3?7KZj-(-m/-D=\m7`=N]
¢ F H
w ®® LT;HgzGLVXd;c@LL>cOO¢
k
S¢<
pr F t k
¢<OL
r F £6t
k
S¢<
pr F £ M
Qt
F S¢ ¡t L?F £ Q2t F S ¢ ¡t F £ MG9jT@Y9ZH*RRSDGCSc@V_d9FWUD
^_LJKJH]_MGa@LT]HgzGL`¢
k
S¢<
pr F
tGL?F£ toF(£¤MuxwvyYz;E¢
F|
Hd;cZEDv¢
k
S¢<
pr
F
uwyYz;E¢
Fb|
VX¦*LjV_ZUL`¢
k
S¢<OL
rF
tjAFÀ£ toL?F(£&M>uwyYz;E¢
F |
Hd]cKWET9Ld^_LJJH;¡tLZEWIH4b9^_VXZET9LZOWUT9LWUT/LDGCELJ¨
PjWjWET9V_Z[;DGV_d@W>a@V_WjV_ZRS^_L>HCjWET]HWOV¢
F
VXZH[/CUV_JLOdlY/J{b]LCWUT/Ld¨Hd@kK[9CUV_JLc@V_z@VXZEDGCjD4
c
V_ZmRSD*d9FGCEY9Ld@WWED
JD9c@Y9^_D
/a@VL*
c
V_ZHdLSh]HGRWj[]DLCD4 /
À##%G #%&('m#\
¡A
¡?¡
jT/Lm[/CUD@DDWUT9LDGCULJ /t\T9LCELCULGY/VXCELZmHZE[]LgRSVH^7WET9LD*CULJ QZULLvu¡t
|
S
"!ª@®; ª $&%('iQ2B D9RE¦@^XV_d9F*WUD*d7§ZWUT/LDGCELJ£S
7AB =T71Y9§-(9VB7G73/:Ee?C BDCE1B h M J p
p
}-mB_C
QJ p g p S M
1j94Z
/:EeACvB_CV1Be?[Y5,24\m7?B7
+
1GeAB[j3-"!1B-D[Y9[
+J
p
-m/#b9{[Y}9 H)(++
[j3`7T1oe?C243-65879E:I58=?7N3
$
ZY-(-DZY-69%
J p
B_CV7N3T77Aab-m/?B1Y9-69IB7G73
¢&$
/A:EeAC§BDCE1B
¢&$('
nqp
MWuxwyYz]
| 1Y94Z Q¢&$
k' nqpr(s)&*
h M g+
S M
@BDCE79 7?1GeAC243-(5>7ZY-(-m/[Y3
[ + -m/>/:EeAC§BDCE1B
MvuxwvyYz;4J
p| H
w ®®®,!ª@®; ª &%P#
- /. 10ª%2«G¥@Y/[9[]D*ZULWUT]H4W¤
¢
V_ZH[/CUV_JLOdlY/J{b]LCg@jT9Ld
c;kmª MYnqpr(s
L f Q
cOg
¤ ¢
SuxwvyYz;I¤
¢ | QZULLvu¡
|
DGCjV_d9ZEWIHd;RSLS
3ÀY9WOT9LCULWUT/L`lH*RSDGb9V§ZjZUk@J{b;DG^V_ZjV_d]c@Ld@WEVRH^7WED LFGLd;c@CULG§ZZUk@J{b;DG^Hd]c"HJD*d9FGZEWfH4^_^
c
ZUY]RETiWET]HWM
c ¤
¢h M*a
Lh/H*RSWU^_k{WET9LT]H^Ï H4CULOZUY]RETWUT]H4W
f Q cOg
¤ ¢ S
MjT/VX^_LOWUT9LDGWET9LCjD*d9LZHCELZEY]RETiWUT]H4W
f Q cOg
¤ ¢ S
ih
M*9¥@D+WET9LCELLSh9V_ZUWUZ
c
ZEY]RETWUT]H4W
cEkmª MYnqpr(s
L
th
M>uwyYz;I¤
¢I|
H4d]c
f Q cOg
¤ ¢ S
¦h MG
4Kª9ª9g50«jxjDZEY9[9[;DGZUL WUT]H4WiWUT/LCUL LSh9V_ZUWEZ
c
ZUY]RET WUT]H4W
f Q cOg
¤ ¢ S h M Hd]c
cEk0ª MGnqpr(s
L h M uxwvyYz;,¤
¢o|
jT/Ld (LT;HgzGL§¤
¢h
M J p
p
jV_WET J p t M H4d]c
p t M £rMG¥@D c kmª
M nqpr(s
L h M h
tiuxwvyYz;¤
¢I|
H4d]c&WUT9Ld Q
cEkmª M nqpr(s
L h M
g+
S Q2t
g+
S63ÀY9Wib@k c@L]d9V_WUV_DGd
V_ZDnc/c¤ZUD¦Q
cEk0ª M nqpr(s
L h M
g S
M*D*CULDz*LC
c;kmª M nqpr
Q h MSL
M`uxwvyYz;G¤
¢I|
G¥@D+H*RRSD*CIc@V_d9FWUD+B D9RE¦@^XV_d9F*WUD*d7§ZWET9LD*CULJ LzGLCEk[9CEVXJKLfcnVXz@V_ZUD*Cq{D4q¤
¢
V_ZZUY;RUTKWUT]H4W
M>uxwvyYz;]tj
M |
LWOY9ZZEY9[9[;DGZULWUT;HW¤
¢
T]HZHWj^_L>HZEWWD[9CEV_JLmcnVXz@V_ZUD*CUZ
p M£
c p tj
M
Hd;c>
L, M(£
c L
¡tY
M
jV_WET
c p g?c L d
M*7jT9Ld¤
¢ d QIM£
c p
¡tY
M
S?QIMO£
c L tj
M S d
QIMO£ tj
M
SL
G
M £ t/tj
M £ M87 ¤ ¢
¥nDi(LT]Hgz*LH
RDGd@WUCSHGc@VRSWEVXD*dH4d]cKWUT@Y9Z¤
¢
V_ZH\[9CUV_JLOd@Y9J{b]LC>
D{RSDGJK[9^_LWULOWUT9V_ZjZULgRSWUV_DGd"VXWZUY RSLZWUDZUT9D¤WUT;HWjLwH4^_fHgk@ZT]HgzGL
f
Q2}
g ¤ ¢ S MG
w ®®+®,+!ªl®; ª O%P PjWO]CUZEW+L{d9LL>c WEDiRSDGJK[9Y9WUL{WET9L{CULJHV_d]cnLCDjWUT9Lc@V_z@V_ZUV_DGd"D¤
¢
blk}9;p
t9
c a
c d
MGa WUT9Ld6 oLTF
Q GLSF
MF
MuwyYz;q
| jT9Ld6tj:9;
t uwyYz;} |
QV_d]c@LL>c tj
MWuxwyYz]¡}
|
S7jT/Ld ¤
¢
toLj£ t\£ M u
t§uxwvyYz;¡}
|
p
t9
c £ M*a c d
a LDGb/WIHV_dV_d H ZUV_JV_^HCjHgk tj 9;
uxwvyYz;¡}
|
H4d]cWET9Ld
¤
¢8
GL£ £ M
>uxwvyYz;¡}
|
jT9Ld a@VXd{b;DGWETRH4ZULZgaE¤
¢
VXZCUL^H4WUV_zGL^Xk[9CEVXJKLjjV_WUT}Hd]cLmRH4dH4[9[9^_k+WET9L*Y]HGc@CSHWEVR
CEL[9CEDnRVXWkK^Hg Hd]cKWET9Ldq
f
Q2}
g ¤ ¢ S Q h MS&<>=%?
9
(@
M =%?
9 f QD¤
¢ g }oS
Q h
MS
ª
MGnqp
f
Q_¤
¢qg }GS
3ÀY9W¤
¢h
MjV_ZLzGLdHd;cWET9Ld
f
Q2}
g ¤ ¢ S f QD¤
¢ g
}GSgjT9Ld{VjV_ZZUY;RUTKWUT]H4W¤
¢>
uxwvyYz;¡}
|
aWET9Ld
f
Q2}
g ¤ ¢ S f Q
g
}oS
POZ(L{T]Hgz*L+ZELLd
tKDGC 9 3ÀY9W
f
Q2t
g
}oS
f
Q2
g
}oS
¨h
MGaZEV_d]RSL}KV_ZwHK[9CEV_JLdlY/J{b]LCHd]c"d9LV_WET9LC+tKd9D*C+ KVXZH
*Y]H*c@CIH4WUVRjCELZUVc@Y/LJD9c@Y9^_D+}/
À##% #+%&'#+\
¡
pdD*CIc@LCjWED{[9CUDz*LWUT9LWUT/LDGCELJ 9]a*Lm[/CUDzGLO]CEZUWE^XkWET9Ld9LSh9Wj^_LJJHE
˻ &%('
7AB
=?71Y9-(9VB7G73?@BDCE79
¤
¢<
p
uxwvyYz;¤ ¢ | H
w ®®LCUVÏk{WUT;HW¤
¢I
p
(£ ¤ ¢
^Q2tY
M h tj
M
£t/tj
M h
toS
jT/LdblkHdKDGb@z@VXD*Y9ZCUL>RSY/CUCULd]RSL{LDGb9WSHV_dq
˻ &%P#
7AB
1j94Z
w
=?7`-69IB7G73A//:Ee?CB_CV1B
7 w d @B_CV7N9
¤
¢v
uxwvyYz;¤
|H
w ®®®,!ªl®; ª &% LW
Hd]cwb;L{VXd@WELFGLCEZZUY;RUTWET]HW
7 w d
;jT9LdH*RRSD*CIc@V_d9FiWED^XLJJH9¡t/a]WET9L
F*CUL>H4WULZEW(RSD*JJD*dc@V_zlV_ZEDGC7D4 ¤ ¢
H4d]c¤ c@V_z@Vc@LZ 94jT9Ld{V_WVXZLV_WET9LC( Hd;cM* 3Y/W( GF VXZD9c9cHd]c{toL
p
tuwyYz; |
H4d]c{WET@Y9Z¤
¢8
tGL£ tj£6M
u
MuxwvyYz;9
|
@jT@Y9ZjWET9LFGCEL>HWELZUWRSDGJKJD*dc@V_z@V_ZUD*C(D4¤
¢
H4d]c¤ V_ZjL *Y]H^WEDiMG
À##% #+%&'#+\
¡
jT/Lm[/CUD@DCULGY/VXCELZWET9LODG^_^_DjV_d9F^_LJJHE
˻ {%('
7AB
=?71Y9-(9VB7G73B_CV7N9 tjM!
?
M>uwyYz;E¤
¢V|
H
w ®®LCUVÏk{WUT;HWtYM"!
? h M ¤ ¢
^QtYM
h
MS
w ®®®,!ª@®; ª &%P LW b;L H"[9CEVXJKLc@V_z@VXZEDGCD¤
¢
jT9Ld6HGRRSDGCSc@V_d9F¨WED¨WET9L[9CULzlV_D*Y9Z{^_LJJH@a]LT]HgzGL
tj
M"!
?
M>uxwvyYz;Y
|
LW
c
b]LWET9LD*CIc@LCOD(tV_dWUT9LJ{Y/^XWEV_[9^_VRHWUVÏzGL]L^c$#&%;9jT9Ld
c
cnVXz@Vc@LZ 4¢<
p LWjY9ZZEY9[9[;DGZEL
WET]HW
c(' 4¢<
p
a/WUT9Ld L(D*Y9^cKT]HgzGLtY
M
M>uwyYz;G
| 3Y9WOWUT9V_ZOVXJK[9^_V_LZX¤
¢v
ML£¤M(£¤M
uxwyYz]o
|
Hd]cWET@Y9Z
93ÀY9WHZjLT]HgzGLOZULLdiV_dWUT/L[9CUD@D4D 9]a@ {c@V_z@Vc@LZd9DGd9LD4WUT/L ¤ ¢
9¥@D{LT]HgzGL
c ¢I
p
3ÀY9WjZUV_d]RLV_ZH
[/CUV_JLjd@Y9J{b;LC(LOT]HgzGLH^_ZED+
)onqp
MuwyYz;Y
|
Hd;c{WUT@Y9Z
c
c@V_z@VcnLZ
h
M*a@VL*9 ¢<
p
c@V_z@VcnLZ
h
M*@jT9V_Z(LZUWIH4b9^_V_ZUT9LZ
WET9LWUT9LDGCULJ¨
) *
i Ài
jT/LmZEVÏh]CEZUWd@Y9J{b]LCUZjDWUT9L\ZULCEVXLZmLCELL>HZEkWUDRET9L>RE¦KDGCj[/CUV_JH4^XV_Wk@PJKDGd9F*ZUWWUT9LJD*d9^_kv¤,+
u/aE¤
p
uG 9a;Hd]c
¤
L
t-*t-*}Gu{H[/[]L>H4CUZWUDKb]L[9CEVXJKLGI¤
ZU[/^XV_WEZL>H4ZUV_^_kV_diWET9CULL2H*RSWUD*CUZDGd"FGLd9LCIH^[9Y/CU[;DGZULZZUk@J{b;DG^_VRRSD*J[9Y9WSHWEVXD*d
ZEDWjHCELG¤
ZE[9^_V_WUZVXd@WEDDGY/C2H*RSWUD*CUZb@k B DG^_^HCSc§ZCUT/D¨JKLWUT9D9c u |
VXd ^_LZUZWUT]H4d M
JV_d@Y9WULZDGdH ¥@[]H4CIR/.U¥@WIH4WUV_DGd
QHZEZUY9JKVXd/F+B DG^_^HCIc §ZRSDGd>oL>RSWUY/CULGu |
S@jT9LY9d@HGRSWEDGCULgc[;HCUWjD4¤10mRDGY9d@WUZMg
c@L>RSV_JH^c@V_FGV_WUZjHd]cV_WUZ2H*RSWUD*CUV32>HWEV_DGdV_Z
Y/d9^_VX¦*L^_kKDGCWUT/L{WUV_JLb;LV_d9F{7HKWUCUVH4^(c@Y9CEVXd/FWD(LL¦@Z+CELzGL>H4^_ZY9d9ZEY]RRSLZEZY/^2 jT9L{WSHb9^_LiMZUY9JKJH4CUV32LZOWUT9L{ZELWD
d/DGdWUCEVXz@VH^c@V_z@VXZEDGCEZjD*CjWUT9LV_dlWELFGLCUZ¤
¢
jV_WUT
'
@jT9V_ZWSHb9^_LGa;^_LWmH4[]HCEWWET9L+RH4ZULZjT9LCEL
jHZODGb9WSHV_d9L>c
b@k{WELZUWEVXd/FHd@k{d@Y9J{b;LC¤
¢
DGCcnVXz@V_ZUV_b9V_^_V_WkjV_WUTiH^_^d@Y9J{b;LCUZjtG ¡ ¢I
p
£¤M DGCM" MG¡} M
;9D*C(d@Y9J{b;LCEZDGC
jT/VRET{WET9V_ZZUL>H4CIRETjHZÀY9d9ZUY;RRSLZEZY9^a@WET9LY9[/[]LCb;DGY9d]cD47ZUL>H4CIRETjHZÀCIHV_ZEL>cWUDM*¡}KM
Àb9Y9WÀd9D+HGc/c@V_WUV_DGd9d;H^9c@V_z@VXZEDGC
jHZÀD*Y9d]c54Od9^_kzGH4^_Y9LZjDiHCELCUL[;DGCEWUL>c
1Y9E9;-De 1o[Y:oB7N3
!
"
#
##
$&% ('*)+-,.%/'0%1
2#3
$&% ('*)+-,.%/'0%1
2#3
-
$&% ('*)+-,.%/'0%1
2#3
$&% ('*)+-,.%/'0%1
2#3
$&% ('*)+-,.%/'0%1
2#3
$&% ('*)+-,.%/'0%1
2#3
45 $&% ('*)+-,.%/'0%1
2#3
45 $&% ('*)+-,.%/'0%1
2#3
-
645 $&% ('*)+-,.%/'0%1
2#3
-
45 $&% ('*)+-,.%/'0%1
2#3
7#
Hb9^_LMG OV_zlV_ZEDGCUZDWET9LZULCEVXLZ¤
¢
D*C
*|
I ,$
\>> E iÀ# >\
pdu¡}
|
aG¥@V_LCE[9V_d9ZU¦@V;[9CUDz*L>cWUT;HWWET9LCULOLSh9V_ZUWUZzGH^_Y9LZ
c
ZEY]RETWET]HW
c
t4¢£¨M VXZÀd9LzGLCfH[/CUV_JLd@Y9J{b]LC>gjT9L^_L>H4ZUW¦@d9Djd
zGH4^_Y9L
c
H4ZUZUY/JV_d9F{WUT/VXZ[9CEDG[;LCUWk"VXZV_d2H*RSWmu*vG}*}Gu9/pWVXZH^_ZUDRSDGdgoSL>RSWEY9CUL>c°WUT]H4WV_WV_ZV_d]c@LLgciWET9L+^_L>H4ZUWd@Y9J{b;LCjV_WUT
WET9V_Z[9CEDG[;LCUWk@V_¦*LjV_ZULGaL{[9CEDzGL{V_dWUT9V_Z[]H4CIHF*CIH4[9TWUT]H4WWUT/LCULKLSh9VXZEWUZzGH4^_Y9LZ+ ZEY]RETWUT;HW+t*7¡ ¢£ MVXZ\d9LzGLCH
[/CUV_JLjd@Y9J{b;LCjHd]cWUT9LCELV_Z(d/D+[9CEV_JLjd@Y9J{b;LCfcnVXz@Vc@V_d9F+H4^_^]WET9LWULCEJZDWET9V_Z(ZELCUV_LG/jT9L[9CUD@D4V_Z(V_dKVXWEZjDGY9WE^_VXd/LZ(WET9L
ZSHJKLmHZ¥nVXLCU[9V_d9ZE¦lV§ZDGd9Lb9Y9WjV_dWUT/VXZRHZUL\(LT]Hgz*LZUD*JLHGc9c@V_WEVXD*d9d]H4^WUL>RET9d9VRET]H4^7[9CEDGb9^_LJKZ>oLT]Hgz*LwH4W]CUZEW
˻ &%('
9E]>-(9IB7j7N3 Y73-X7?/K1bBX\P7?1/?B[Y947[
+
BDCE7
+
[j\(\P[j}-(9%>eT[j9%Y3:E794e?7A/
! "$#&%('
! "$#&% )'
* "$#&%('
! "$#&%('
! "$#&% +'
! "$#&% +'
! "$#&% +'
$ "$#&% )'
, "$#&% ('
-- "$#&% ('
$ "$#&% ('
w ®®QpW7oSY/ZUWjZUY RSLZWED{zGLCEVÏk{WUT9V_ZD*CHd@k{V_d@WULF*LC
lu/
DGCULDzGLCga9LmT;HgzGLG
˻ &%P#i)(+z/.
-m/,/:VeACBDCE1B GF
oF10vuxwyYz£z
| @qB_CV7N9
z
ZY-6-DZo7?/
20
h
MoH
w ®®y¥@Y/b9ZUWECIHGRWmHd;c{HGRSWEDGCUV32L*
jT]H4Wj^_LJJHRH4dib]LY9ZEL>cWED{LZUWSHb9^_V_ZUTWUT/L;CUZUWO[]HCEWjDWUT9LWET9LD*CULJ
"!ª@®; ª 3&%(' U
CV7N3T7"-m/`94[>-(9VB7G73 z 7 M
/:Ee?CB_CV1bB
z
ZY-(-DZG7A/K1Y\(\{B_CV79E:I5>=T7N3?/
tG ¡ ¢£ MoH
w ®®QpWV_Z(V_JJKL>c@VHWEL(WET]HWd9LV_WET9LCt\d9DGCj +cnVXz@Vc@LH4dlY/J{b]LCÀDWET9LODGCEJ tG 4¢f£ M*9xjD VÏz76 c@V_z@Vc@LZjHd@k{D
WET9LZELWULCEJZjWET9Ldzc@V_z@Vc@LZj
p h M
tjT9VRETV_ZjVXJK[]D*ZUZEVXb/^XL*
3Àk^_LJKJH|9¡t9a*LmZET9D H^_ZUD{
"!ª@®; ª 3&%P#
[Y3K1j\(\O-(9IB7j7N3c{@1B\P7?1b/TB[Y947>[
+
B_CV7
+
[j\(\P[j}-(9%ve?[Y9%Y3:E79{eT7A/`-m/`b7N3-7TZ2
54
* 6"7#5% ('
54
* 6"7#5%+'
54
! 6"7#5%+'
4
! 6"7#5% 78'
54 )9, 6"7#5% ('
4 ):, 6"7#5%('
4
);, 6"7#5%+'
54 )<: 6"7#5%='
54 5>?>* 6"7#5%('
54
5>A@, 6"7#5%('
54
)@; 6"7#5%('
1Y9E9;-De 1o[Y:oB7N3
w ®®QjT9V_ZWUT/LDGCELJ LSh9[9CELZUZELZVXd\2H*RSW7LSh]H*RSWU^_kWET9LjZIH4JLRSDGd/FGCUY/Ld]RSLZjHZ^_LJKJH|9_Mb9Y9WV_d+Hc@V LCULd@W2H4ZUT9V_D*d7 LW
Y/Z(ZELLVXWDGd{WET9LO]CUZEWRSDGd/FGCUY/Ld]RSLG/D]d]cKHRSDGd/FGCUY/Ld]RSLDGCj GFCELZU[;L>RSWEL>cb@kH^_^;zGH^_Y9LZ
c
ZUY]RETWUT;HW
c
uxwyYz]@
| a
V_d z@VXCEWUY9L{D4(^_LJJH{|9¡t9a;L{d9LL>c WED]d]c 2H*RSWUD*CUZD4 j
h
MG;pd 2H*RSW>aL{T]Hgz*L j
h M
t/_M> 9;jT9L{zGH4^_Y9L8z VXZ\d9DGW
H*RRSL[/WIHb/^XL\ZUV_d]RSLV_WjDGY9^c^XLgHGcKWUD{WET9L+RSD*d9FGCEY9Ld]RSL{ GF
M>uxwvyYz;9t
|
a@WECUV_z@VH^_^_k{CULZE[]L>RWUL>c b@kH4^_^VXd@WELFGLCEZ
c
Hd;cWET@Y9Z
DGY/^cCULd;c@LCmH4^_^WUT9LD*WUT9LCRSDGd9F*CUY9Ld]RSLZY9ZEL^_LZUZg V_¦GLjV_ZULOD*CHCUL>H4ZUD*dWET]HWjjV_^_^b;L+RS^_L>HCjV_dKWUT9Ld/LSh9WWUT/LDGCELJL
d/LL>cic@V_ZEWUV_d]RSWjJKDncnY9^_V]V_dCUV_FGT@W.2T]H4d]c{ZEVc@L+Hd;cWET@Y9ZjWUT9V_ZjLSh9[9^H4VXd/ZjWUT9L[/CULZELd]RSL{D4 Y@v9MOZUV_d]RSLH^_^WUT9L\DGWUT/LCUZOZUJH4^_^XLC
HGRSWEDGCUZjD4 oL
h
MHCULH^_CUL>H*c@k{Y9ZEL>c
LOT]HgzGLWUT/Ldq
"!ª@®; ª 3&%P
[Y3K1j9E]>-(9IB7b3?1Y\OY1Y\:E7,c{@
oF
h
tGt*vGv*}G}Y@|G * GtG} Gu}*|GtGtt Y@t
-0/e?[j52E[/-mB7
H
w ®®QpX¢KV_ZmHdLz*Ld dlY/J{b]LCjZEDG^_Y9WEVXD*dDWUT9L\ZUk@ZUWELJ D4 WET9LD*CULJ |/t/a@CUL[/^H*RSV_d9F oFb@k£¢KWUT9Ld¨ GF
h
¢KV_ZmH^_jHgk@Z
cnVXz@V_ZUV_b9^_Ljb@kH4Wj^_L>HZEWjDGd9LDWUT9L\JD9c@Y9^_V 3ÀkZUD*^_zlV_d9FWUT/LmZEk@ZUWULJ (LO]d]cKWET9L+Hb;DzGLOzGH^_Y9LG
jT9V_ZWET9LD*CULJ Lhn[/^H4V_d9ZjT@k+Ljd9LLgc@L>cc@V_ZUWEVXd;RSWJD9c@Y/^XVgV_d{DGCSc@LCWUDT]Hgz*LHZUD*^_Y9WUV_DGd\D*CWUT9LRSDGd/FGCUY/Ld]RSLZUk@ZEWULJ
WET9V_ZRSDGd;c@V_WUV_DGdKVXZjd/L>RSLZEZIHCEkl
6V_WETWUT/VXZjWET9LD*CULJ LJHgkZUWIH4WULG
"!ª@®; ª 3&%
[Y3£1j9E]-(9VB7Y3T1Y\b1j\:E7c{@
GF
M>}*}-9MNl|/Ml| Gv* YG}
}Gu
uG}Yj£ M
-m/veT[j52E[/-mB7 H
[Y3?7T[jb7N3B_CV7 /7?BK[
+
-69IB7G73A/
/A:EeACvB_CV1bB t*
GF£¤M
-m/K1Y\}1Y]/Ke?[Y5,2V[b/A-0B7A@CV1/>12E[/-mB-(b7ZG7N9I/-mB] H
w ®®Qp F h ¢ V_ZH4^XjHgk@Z+c@V_z@V_ZUV_b9^_L{b@kHW^XLgHZUW{D*d9LJKD9c@Y9^_Va]ZEDV_ZH4^XZEDD*C¡ F £ MKjT9LCUL
h ¢ nqp
V_dWET9L
J{Y/^XWEV_[9^_VXRH4WUV_zGLFGCEDGY9[{D4WUT/Lm[/CUD9c@Y]RSW¤D4H^_^;JD9c@Y9^_V13kKZUDG^_z@V_d9FWET9LL *Y]H4WUV_DGdK(L ]d]cKWUT/LmHb;DzGLOzGH^_Y9LGID*CULDz*LC
WET9V_Z(zGH4^_Y9LRH4db]LV_d]RSCELJLd@WEL>c{b@kHd@k{J{Y9^_WEVX[/^XLÀD t Q ¤V_Z(D9c9c;S@pWjVX^_^;ZUWEVX^_^;FGV_zGLHdKLzGLdd@Y9J{b;LC(H4d]c{DGd7§W
H LgRSWWET9LRSDGd9F*CUY9Ld]RSLZgjT9V_Z([;DGV_d@WjLZEWIHb/^XV_ZET9LZWET9LZUL>RDGd]c[;HCUWjD4WET9LWUT/LDGCELJ¨
DGCULDzGLC
"!ª@®; ª 3&%P
7?B=?7>1Y9E]-(9IB7>G7N3 Hq)(++
[j3K1Y\(\-(9VB7G73c }-mB_C c
*@u
@
oFj£
-m/8Zj-(-DZG1o=\m7>=]1B\P7?1b/TB[Y9{7v[
+
B_CV75>[Zj:<\^-[
+
B_CV7"/]/TB7N5 [+
BDCE7?[Y3T7N5 H
@B_CV7N9
+
[j3`1Y\(\{c{@
GFj£
-m/KeT[j52E[/-mB7
H
w ®® LW zKb;LJD9c@Y9^_DDWUT/L+ZEklZEWULJ 3Àk^XLJJH\|9¡t9aEzc@V_z@Vc@LZ 0 h
M\jT9LCEL V_ZH{JKD9c@Y9^_D+D4WUT9LZEk@ZUWULJ D
WET9LD*CULJ |/XM* 3ÀY9WOVXdWET9V_ZRHZEL V_ZH{c@V_z@V_ZUD*CjD@v99/DGCH4dlk¢ 7 MHd;cH4d@k
c
aE¢IF
h
MV_ZH^_fHgk@Zjc@V_z@VXZEV_b9^_Lb@k£¢
h
M*
POZH{RSDGd/ZUL *Y9Ld;RSL 20
h
Mc@V_z@Vc@LZ
p L + h
MH4d]c{WETlY/Z z{c@V_z@Vc@LZ Y
h
M*]x D6VÏLmZEY9[9[;DGZELWUT]H4W GFj£
DGCjHFGV_zGLd
c
Hd]ciHKF*VXz*Ld
V_Zc@V_zlV_ZEVXb/^XL\blkz;a;WUT9Ld H4dlkd@Y9J{b;LCD4(WUT/LD*CUJ oF
p L + £
V_ZH^_ZUDc@V_zlV_ZEVXb/^XLb@kWz;E&T9Ld]RSL{WET9L
CELZUY/^XWg
¥nD+LT]HgzGLG
®; ® / « &%('
[Y3`1Y9E]-(9IB7b3?1Y\OY1Y\:E7,c{@
GF
M>}*}-9MNl|/Ml| Gv* Yl}
}Gu
u}Y£&M
1Y9{Z
GFj£&M>}*}-9MNl|/Ml| Gv* YG}
}Gu
uG}Y
1j3T7`1j\}X1j]/KeT[j52E[/-mB7
H
w ®®y/DGCH^_^ VXd@WELFGLC
c
jV_WUT
c
ilu/a oF£\VXZc@V_z@Vc9Hb/^XL\blkiH4Wm^_L>H4ZUWDGd/L+D4fWET9L+JKD9c@Y9^_V7D4(WUT9LZUk@ZEWULJD
WET9LD*CULJ |9¡tHd]cKWUT@Y9ZjWET9L[9CELz@V_DGY9ZjWET9LDGCELJ H[9[9^_V_LZg
PjW WUT9V_Z7[;DGV_d@WZULzGLCSH^ *Y9LZUWEV_DGd9ZHCUV_ZELG7V_CEZUWU^_kjT]H4WVXZ WUT9LÀ^XLgHZUW zGH^_Y9L\ZUY]RETWET]HWtG
GF*£{MV_Z7H^_jHgk@Z7RSDGJK[]D*ZUV_WUL
jT/VXZ GY/LZUWEVXD*d{V_ZZUWEVX^_^9Y/d9ZUD*^Xz*L>c\D*CWUT9LRHZELD47[]DLCUZÀDtH4^XWET9DGY/FGTWUT9LOVXd@WELCUzGH4^9D7CELZUL>H4CIRETV_ZJ{Y]RET+JKDGCEL(CEL>c@Y]RSLgc
u
|
¥@DjV_WUT9D*Y9WHGc9c@V_WEVXD*d9d]H4^7WUT/LDGCELWUVRH4^(CELZUY9^_WEZ>a VXWV_Z*Y9V_WUL{RS^_L>HCWUT;HWWET9V_Z *Y9LZUWUV_D*d¨jV_^_^d9DGWb;LHd9ZE(LCEL>c V_d¨WET9L
d/L>HCY/WUY9CELG
4Od9LjHd9D*WUT9LC *Y9LZUWUV_D*d+HCEVXZELZ*RHdLT]Hgz*LfRDzGLCEVXd/FZULWUZD RDGd9F*CUY9Ld;RSLjjV_WUT^_LZEZWET]HdKMGMJD9c@Y/^XVjT/VXZ*Y9LZUWEV_DGd
JH¦*LZZELd9ZUL{ZEV_d]RSL{ZUV_d]RL{WUT9LDGCEVXF*V_d]H^LSh]HJK[9^_LD¥@V_LCU[9V_d9ZE¦@V7DGC[]DLCEZDftRSD*Y9d@WUZ+uJD9c@Y9^_VHd]c"V_WjHZ[9CUDz*L>c
H WULCWUT;HW,JD9c@Y9^_VZEY RSLVXdK2H*RSW>;pWOVXZH^_ZUD{d/DGWUL(D*CUWUT@kiWET]HWOWUT9LRHZEL{D[]DLCEZmD4( {V_ZWET9L+DGCEZUWOVXd"WUT9V_ZZELd9ZEL
ZEV_d]RSLODGCjT/VXF*T9LCj[;D(LCUZj^_LZUZOJD9c@Y9^_VHCELmd/LL>c@L>c
jT9L\LSh]HGRSWc@LWELCUJKV_d]HWEVXD*dD4 WET9L^XLgHZUWOd@Y9J{b]LCjDJD9c@Y9^_VDGY9^cCUL *Y9V_CUL{H{T@Y9F*L+HJKDGY9d@WD(RSD*J[9Y9WSHWEVXD*dWEVXJKL
b/Y9WHZjLZUT]H4^X^ZELLV_dWET9Ld9LhnWEV_DGdZUL>RWUV_DGdV_WjV_Zj[]D*ZUZUV_b9^_LWUD[9CEDzGLWUT]H4WjWUT9V_Zjd@Y9J{b;LCVXZH4Wj^_L>HZEW}9
*O ¥ O
m\7Ki #+% # "
V_CUZEWU^_k{WUT/LDGCELJ |9_MO[9CUDz*LZjWUT]H4WHWj^_L>H4ZUWjWD+JKDncnY9^_V H4CULd9LL>cnL>c V_¦GLjVXZEL(LT]Hgz*LmWET9LODG^_^_DjV_d9FWUT9LDGCULJW
"!ª@®; ª 'O%6' U
CV7eT[jb7N3-(9 K/7AB[
+
e?[j9%b3N:V7N94e?7A/8[
+
B_CV79E:I5>=T7N3?/
tG ¡ ¢£¤M
e?[j:<9VBD/K1B\P7?1b/TBv9E:I5>=T7N3?/
H
pdWET9LD*^X^_DjV_d9FLjV_^X^;Y9ZELWUT9L\d9DGWSHWUV_D*dD(¥@WSHd@WUD*d§uu |
WUD{V_^_^_Y9ZUWECIHWELWUT9LRSDz*LCUV_d9F{ZELWD4 WET9Ld@Y9J{b;LCUZt*7¡ 4¢m£6Mo
WET9LZUY]RRSLZUZEV_zGL dlY/J{b]LCEZHCELCEL[9CELZULd@WEL>c¤b@kH CUD D4\RL^_^XZH4d]cHRL^_^mRH4d RDGd@WIH4VXd DGd9^_kd@Y9J{b;LCUZcnVXz@Vc@V_d9FiWET9L
RDGCUCELZU[;DGd;c@V_d9F{WULCEJ V_dWUT/LZULCEV_LG9POdV_JK[]D*CUWIH4d@W2HGRWjVXZjWED{b]Ld9D*WUL>c&
]'&%(' U
CE7`9;:<5>=?73
ZG[7A/"9{[B =?7\m[Y9%B[B_CV7eT[jb7N3-(9 `/7?B
H
pd;c@LL>cV_WV_ZRS^_L>HCjWET]HWt{RH4d9d9D*Wc@V_zlVc@LHd@Y9J{b]LC(D4WUT/LDGCEJ G ¡t¢£6MG
w ®®y V_CUZEWU^_kV_d+z@V_CUWEY9LjD^_LJJH(|/¡t9aHOdlY/J{b]LCRH4d9d9D*WZEY]RRSLL>cKWUDV_WUZUL^S LWY9ZÀZUY9[9[;DGZELWET]HWDGd/^Xk\W(Dd@Y9J{b;LCUZ
DGCUJrWUT9LRSDz*LCUV_d9F{ZELW>/jT9Ldid9LgRSLZUZSHCEVX^_kWUT/LwRDGd9F*CUY9Ld;RSLZDWUT9LWELCUJKZjDWUT9LZULCUV_LZHCELwH4ZDG^_^_DjZ
P 3 P 3
3ÀY9WWUT9LdV_d{z@V_CUWEY9LD4^_LJJH|/t/aY¤ Hd]c c@V_z@Vc@LZj GL
h
MG%3ÀY9W GL
h M
vV_Zjc@V_zlV_ZEVXb/^XLjb@k{t+H4d]ct\c@D@LZjd9DGWb;L^_DGd9F
WED{WUT9L\ZULWg ¥nD{WUT9LCELV_ZHRSD*d@WUCIH*c@VRSWUV_D*d799CEDGJ WUT9V_ZjLJHgk{H^_ZED{d9DGWELmWET]HWOWUT9L\D ZULWOb]LWLLd ZUY;RRSLZEZUV_zGL[9^HGRSLZD
H\ZIH4JLOdlY/J{b]LCjRH4d9d9DGWOb]LL *Y]H4^7WEDt/
x D ^XLWmY/ZZUY9[/[]D*ZUL{WUT;HW(LT]Hgz*L+WET9CULL{d@Y9J{b;LCEZ¤+a{a V_d WUT9LZULWg7¥@V_d]RSL{WET9L[]D*ZUV_WUV_DGd"DH{ZIH4JLd@Y9J{b;LC
RHd9d9D*Wc@V LCjDfMD*CjDt9a@d9L>RLZUZSHCUV_^_kWUT9LwDGY9CÀ]CEZUW^_D9RH4WUV_DGd9ZV_dWUT9LCUD HCELZUDGJKLWUT/VXd/FH4ZDG^_^_DjZ
P 3 P
3ÀY9Wd9D WET9L9WET{^XD9RH4WUV_DGd{RH4d9d9DGWRSDGd@WIH4V_d+d9LVXWET9LC¤6d9LV_WET9LC{*¥@Dd9L>RLZUZSHCUV_^_k{V_WRSDGd@WIH4V_d9Z Hd;cWUT9Lj^_D9RHWEV_DGd9Z
D4(b;DGWUT¤ Hd]c c@V LCEZCEDGJ];jT9LdVXd"zlV_CEWUY9LD(^_LJKJH|9¡t{b;DGWETW¤ H4d]c c@V_z@Vc@LZ Y
h M v 3Y/Wwv
T]H4Z
D*d9^_k{DGd9LD9c9cc@V_z@V_ZUDGCjHd;cWET@Y9ZjkGD*YT]Hgz*LwH{RDGd@WUCSHGc@VRSWEVXD*d7
¥@Y/[9[]D*ZULd9D6WET]HWLmT;HgzGLjDGY9C[9CUV_JKLZ>*jT9LdKWUT9LO]CEZUWD*Y9C(^_D9RH4WUV_DGd9ZD7WET9LCUD RHdT]HgzGLOW(D{RSD*d@]FGY/CIHWEV_DGd9Z
LVXWET9LC
P 3 P
D*C
P 3
LWY9ZOWUCEL>HWOWUT9L;CUZUWRHZELG;jT9LO9WETi^_DnRHWUV_D*dRH4d9d9DGWOWUT9Ldib]L¤ QD ZULW+MSa¨QD ZELWtGSd9D*C{;pd]c@LLgcV_dWET9L
^H4WUWULCfRH4ZULOVXd{z@V_CUWEY9LD47^_LJJH|9¡t/ab]D*WUT¤ H4d]c ZET9DGY9^cKc@V_zlVc@L j
h M
t9_M> wjT9VRUT{V_ZV_J[;DGZUZEV_b9^_LGgjTlY/Z(WET9LO9WUT
^_D9RH4WUV_DGdRSDGd@WIH4V_d9Z
P 3 P
jT9LdWET9LZUVÏh9WUT[;DGZUV_WEVXD*dRH4d9d9D*WfRSD*d@WIHV_d¤RQD ZULWmtGSa QD ZULW V_dRDGd]RSY/CUCULd]RSLjVXWET¤ SÀd9DGC QD ZELW+MS9¥@D
LT]HgzGLo
P 3 P 3
jT/LmZELzGLdlWETi[;DGZUV_WEVXD*dRSD*d@WIHV_d9ZjWET9Ld¤ ZEV_d]RSLWUT9V_Zjd@Y9J{b;LCT]HZH4dD ZELWLGY;H^WUD ;
P 3 P 3 P
jT/LdWUT9LLVXF*T@WUT[;DGZEV_WUV_DGdRHd9d/DGWmRDGd@WIH4VXd¤+a d/DGC Q2RSD*d]RSY9CECULd]RL{jVXWETv¤SjHd]cKWUT@Y9ZRSDGd@WSHV_d9Z{
P 3 P 3 P
jT/Ld¨WET9L{d9V_d@WUT []D*ZUV_WUV_D*d¨RSDGd@WSHV_d9Z 3ÀY9WWUT/Ldb]D*WUT Hd]cT]HgzGLiHZD ZULWjT9V_^_L+ Y
h
M\T]HZ\DGd9^_kDGd9L{D9c9c
cnVXz@V_ZUD*C>*jT9V_ZjLZUWSHb9^_V_ZUT/LZWET9L+RSD*dlWECIH*c@VRSWUV_DGdDGCjWET9LO]CUZEWmRH4ZULG
jT9L{ZEL>RSD*d]cRH4ZULKZU[9^_V_WUZV_dW(DZEY9b RHZULc@L[;Ld]c@V_d9F DGd jT9LWET9LC(L{[/Y9W`¤ D*C V_d¨WET9L9WET[]D*ZUV_WUV_DGd PZWET9L
CEL>HGcnLCJHgk+z*LCUVÏk{VÏWET9L^_LWEWULCjV_Z¤ DGCa9V_db;DGWET RHZULZ>a;(LD*b9WIH4VXdH{RSDGd@WECIHGcnVRWUV_DGdKD*C(WET9LWULdlWET[]D*ZUV_WUV_DGd
jT9V_ZJLWET9D9c{H^_WUT/DGY9F*T{ZUV_J[9^_LV_Z(CSH[9Vc@^_kY9d@L>H4ZUV_b9^_Ljb@k{T]Hd;c{b;L>RHY/ZULD7WET9LJ{Y9^_WUV_[9^_VRHWEVXDd/ZD47ZUY9bRH4ZULZOjT9VRUT
T;HgzGLWED{b]LRSDGd9ZEVc@LCULgc
1Y9E9;-De 1o[Y:oB7N3
m\7 >#K
pdKWUT9V_ZjZEL>RSWUV_D*d7a@(LWSH¦GLOWUT9L[9CEDGb9^_LJ CUD*J WUT9LD*[9[]D*ZUV_WULZEVcnLmHd;cDGd;c@LCjT9LWUT/LCWET9LCUL\VXZd9D{RSDzGLCUV_d9FZULWOjVXWETH
[;LCEVXD9cKZUJH^_^_LCWET]Hdlv/@jT9CUD*Y9FGT/DGY9WjWET9V_Zj[]HCSHFGCSH[9TLjVX^_^7c@Ld9DGWEL WET9L^_L>HZEWjzGH^_Y9LODWUT9L[;LCUV_D9c;LmT;HgzGLHW
;CUZUWjWET9LD*^_^XDjV_d9FWET9LDGCELJW
"!ª@®; ª '{'4%6' U
CV79E:I58=?7N3
-m/`94[B12{3-(5>79E:I58=?7N3
H
w ®®QpL+RSDzGLCmHZULWmtG ¡ ¢£ Mb@kiHZULWD(RSD*d9FGCEY9Ld]RLZjVXWETiH{[;LCUV_D9c {a9V_Wjd9L>RLZUZSHCUV_^_kY9ZULZmWET9L+c@V_z@V_ZUD*CUZjD
h
MG 3Y/WH4ZmL{T]Hgz*L{ZULLd DGd9^_kiD9c9c c@V_z@V_ZUDGCEZ+RH4dH[9[;L>HC\VXd WUT/L{ZULWDRSDGd/FGCUY/Ld]RSLG LW
c
b;L{WUT9L{d@Y9J{b;LCD
D9c9c [9CUV_JLc@V_z@V_ZUD*CUZD4f
h
MWET9Ld d9L>RSLZEZIH4CUV_^_k
c '
9pd]c@LL>ca7HdlY/J{b]LCOjT9VRETiV_Zmc@V_z@V_ZUV_b9^_Lb@k D9c9c[9CEVXJKLZV_Z
F*CUL>H4WULCjWET]Hd @¥@DWUT9LRSDz*LCUV_d9FZULWRSDGY9d@WEZHWJDGZEW
h
MRSD*d9FGCEY9Ld]RSLZ>¥@V_d]RSL T]H4Z(d9Dd9D*dWECUV_z@VH^]c@V_z@V_ZUD*CUZ>a@WET9L
[;LCEVXD9c@VRSV_WkDH^_^9WUT/VXZjRSD*d9FGCEY9Ld]RSLZJ{Y9ZEWb]LL *Y]H4^]WEDGjT9Ldb@kc@Ld9ZEV_Wk{VXWV_ZfR^XLgHCWUT]H4WfH4W(JKDGZUWjMOd@Y9J{b]LCDGY9WD
V_Zjd9DGWjRSDzGLCUL>c
pdHGRSW WUT9LjHCEFGY9JKLd@WD c@Ld9ZUV_WkV_Z7zGLCUk[;D(LCY9^9H4d]cc@V_ZIRHCIcwJDGZEWD]WET9LjRHd]cnVc/HWULÀ[]LCEV_DncnZ>LW @HRH4d]c@Vc9H4WUL
[;LCEVXD9c54OY9CH^_FGD*CUV_WUT/J$WEDRET9L>RE¦VXWjHZjWUT/LDG^_^_DjV_d9F4
]H*RSWUD*C
h
MHZjL^_^7HZ
) h
MODGCjH^_^Eic@V_z@VcnVXd/F
9D*CfH4^X^D9c9c[9CUV_JKL2HGRSWEDGCEZc@V_zlVc@V_d9F
) h
MHd]cd9DGWjc@V_z@Vc@V_d9F+
h
MOjV_WUT\c@V_zlVc@V_d9F,7a9RSD*Y9d@WmMHZRSDz*LCUV_d9F
c@Ld9ZEVXWk@
Pmc9cH4^X^ WUT9LcnLd9ZUV_WEVXLZ>p(WET9L{CULZUY9^_WV_ZZEJH4^X^_LCOWUT]H4dMGa WUT9Ld@Y9J{b]LC RH4d9d9DGWb;LH{[;LCUV_D9cpjWUT/L+CELZUY9^_WV_Z
FGCULgHWULCWUT;HdMWUT9Ld RET9LgRU¦KD*CjWUT9LLSh9V_ZUWELd]RSLDHdLL>RSWEVXz*L+RSDz*LCUV_d9F{ZELW>
jT9L\dlY/J{b]LCEZjjT9LCEL2H*RSWUD*CUL>c blkY9ZEV_d9FviH[/^XLouv |
&4d/LCULJHCE¦V_ZjWUT]H4WT9LCUL(L+H*RRSL[/Wmc@Y9[/^XVRH4WUL>c b]HZEVXZOV_dWET9L
RDGCUCELZU[;DGd;c@V_d9FRSDzGLCUV_d9F{ZULWDWUT9L\VXd@WELFGLCEZjDGdWUT/L+RSDGd@WECIHCEkD4 CScDGZOLSh]HJ[/^XL*
4 ª@ 1024 ª ª LWKY9Z{WIH4¦GL
t
jT9Ld
toL¡}Hd]cjT;HZt9a]a}/ajM
at
HZc@V_zlV_ZEDGCUZgjT9L
CELZU[;L>RSWEV_zGL{RSDGd@WUCEV_b9Y9WUV_D*d9Z(WEDc@Ld9ZEV_WkHCELG
GL
h M
tjd9DRSDGd@WECUV_b9Y9WEVXD*d7
Y
h M
tjG¡} Mj]
0 h M
t/_MGML M*}9
p + h M
tY@_MGMLg9M M/M
GL + h M
tY@¡}GLg_MGML4/MG_MGMgv9M MGt
D*WIH4^7c@Ld9ZEVXWkO MYj£¤M*}(£¤M/M
£6MGt
*}
'
MG
jT/Ld
t
RHd9d9D*Wb;LH[]LCUV_D9cKDGCHRSDz*LCUV_d9FKZULWOD*Cd@Y9J{b;LCUZ G ¡t¢£¤MG9jT/L+CEL>HGc@LCmJHgkd9D*WWET]HWO(LD*d9^_k
T;HgzGLH{JHoSDGCSHWEVXD*d{DWUT/L+c@Ld9ZEV_Wk.;9D*CjV_d9ZUWSHd]RSLV_dWUT9L[/CULz@V_DGY9ZOLSh]HJK[9^_LGa@ZUV_d]RSLHd;ci}{HCELCUL^H4WUV_zGL^_kK[9CUV_JL*a@VXd
HZULWD4Àt
D*^_^XDjV_d9FWULCUJZH4W^XLgHZUWODGd9L\(D*Y9^cT]HgzGL\b]LLd c@V_z@V_ZUV_b9^_Lb@k }KHd]c LGF]7M*MG;PZHRSD*d9ZULGY/Ld]RSLKDGd9L+RHd
CELS]d9L{WET9LH4[9[9CEDghnV_JHWUV_D*db@kiZUY/b9ZUWECIHGRWUV_d9F MY
WEDiWUT9L;d]H^(cnLd9ZUV_Wk ZUV_d]RSL{D*d9L{DjWUT/LRSDGd9F*CUY9Ld]RSLJH¦*LZc@DGY9b/^XL
Y/ZULG
jT9LWSHb9^_LtZUY9JKJH4CUV32LjWUT/LmCELZUY/^XWEZV_dWELCUJKZjDc@Ld9ZEVXWk@
POZL+RHd"ZULLL RHd;c@Vc9HWELZ[]H4ZUZOWUT9V_Zj;CUZUWOWULZEWjVXWETZUY]RRLZUZtj]a9 -/a]H4d]clv9 3Y/WmHZO(LT]Hgz*LZULLd¨LJHgk
CELS]d9LWET9LJHoSDGCSHWEVXD*d79D*CV_d9ZUWSHd]RLjD*CftjT]HZjt9a@ 9aj]a9a@v9a;M>t9a@tYHZjc@V_zlV_ZEDGCUZgGp7LDGY/^cT;HgzGLHRSDzGLCEV_d9FZULWDGC
d@Y9J{b;LCEZ(tG ¡ ¢(£M jVXWETtj+HZ[;LCEVXD9cWUT9LdKV_W(D*Y9^cCULZEY9^_W(V_d@WUDHRSDzGLCUV_d9FZELW(D4RSDGd/FGCUY/Ld]RSLZOD7WET9LZELW(D47d]HWEY9CIH4^
d@Y9J{b;LCEZRSDGd@WIH4V_d9V_d9F H4d]cH4Zb]H4ZUV_ZD4(JD9c@Y/^XV@¥@V_d]RSLWET9DGZEL+WDd@Y9J{b;LCEZmHCELCUL^H4WUV_zGL^XkK[9CUV_JKLGa9D*d9LV_d@WULF*LCDGY9W
D4fMgtDGY9^czGLCEVk{WUT9LWDRSD*d9FGCEY9Ld]RLZ>a;ZUD{WET9LLZUWEV_JHWEV_DGdD*C(WET9Lc@Ld9ZEVXWkKDtY{RHdb;L^_D(LCEL>c{b@k MGtj]*PjW(WET9V_Z
[;DGV_d@WVXWb;L>RSDGJKLZZUJH4^_^XLCWUT]H4dMmH4d]c{WET9LditY{RHdb;Lc@V_ZIRH4CIc@L>cCEDGJ WET9LRHd;c@Vc9HWELZ>V_¦GLjV_ZELWUT/LmLZUWUV_JHWUV_D*dDGC
WET9Lc@Ld9ZEV_WkD -RHdb;L^_D(LCUL>cblk M*tYj£6M*uGt\ZUV_d]RSL{V_ZCUL^HWEV_zGL^_k{[9CEVXJKLjV_WUT +H4d]c|9@jT9LD*b9WIH4VXd/L>cKzGH^_Y9LV_Z
ZEWUV_^_^]F*CUL>H4WULCOWUT]H4dMmH4d]cKZUD{jV_WUTKWUT9V_ZjWULZUWV_WV_ZjVXJK[]D*ZUZEVXb/^XLjWEDRDGd]RS^_Y]cnLDGCWUT/VXZjzGH4^_Y9LG*PdLSh]HGRSWOZUL>H4CIRETiD4 RSDz*LCUV_d9F
T;HZWEDb;L+c@D*d9LG;jT9L\2HGRSWEDGCEV2gHWUV_D*dD4f GF
h
M\(LCEL
c
c@V_zlVc@LZm -F*V_zGLZOWUT9Ld@Y9J{b]LCjD(RSDGd/FGCUY/Ld]RSLZJD9c@Y/^XD
c
WUT]H4W
H4CUL[;DGZUZEV_b9^_LmWEDHGRRL[9W
GL
h M
tj xjDRSD*d9FGCEY9Ld]RSLJD9c@Y/^XDt/