HAL Id: hal-00129671
https://hal.archives-ouvertes.fr/hal-00129671
Preprint submitted on 8 Feb 2007
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.
La Première Méthode Générale de Factorisation des Polynômes
Maurice Mignotte, Doru Stefanescu
To cite this version:
Maurice Mignotte, Doru Stefanescu. La Première Méthode Générale de Factorisation des Polynômes.
2001. �hal-00129671�
! "#$&%' () %*+)(,-/.) %
02143&561'798:;1'<>=@?
A
=B56CD7
A 8
A-EFGHFIKJML 1ON
A
73
P Q$RTS6UWVYXP UWZ\[]^_^`X a(b cd]SeRgfhi^`XOjlkQm[\XOniVOR
oqp
r&sut`v
p
rlwYxeyuz({Y|~}(
{
D
y {O
z( yWz}D
{Y|
zy
z({#
xO&
}
yuz'WW
lYz~
}
WW¡¢'{;z~}#£T¤¥
yu}£{
£y
{4|¦yu£§ ©¨yª
{«Ty
¬
D
{
}D{#W
{;
® z {#}
}D¯
{#
$°
l±e}Dy
(
²
}
³l´Olµ³uz({ª#
{;z~}¶
ª
¨
ª {;z·
°
ª
¸
(y
¤¥
yu}£{
£y
}
yuz¹(ºz
} z
£{
u£z6
{Yº»³
}
{O¼
{
¥½
}|&yW£
¾y
|W}$»³
}
D
{¼
{À¿Á
9
}
i
yuz(
}
|W}±e}Dy
(
²
}ÂÃ
®
zi#z
£{~
¥½
}|¦yu£
¾y
O°
W}D
°Ä
{e
z $|}Dy&
i
{e|
}Dª
¤Å
yW}£{
}
{e|&yW£§
l¨
yª
{Yy
{³
W}
{
{ey
D¬
{Y{y
|
{KÆ
u£yu}
(ª
®
z~©yª
¸
{6}
{;z~
{e
}
yWz~£¹¯z(
}
'
±e}Dy
(
²
}³Ç
yu
z$|(u}³e(µeuz({ª#
~
ªÇ
(y
T
{
|z{
¬
|&yWz~}"
{O|&yW£§ l¨yª
{"{
u
{HÈ
{ }DyW£{ªÇ
y
{{y
}¥« ª yªO|W} {³u e {³u£yW}ª {Yª#y } {e ¤¥ yW}£{ £y
ÉTÊ
suËÌÍÏκË(wÁÐ
|}
{
;Ñ y6
² y
ÑÒ
|W|
}D{yu¤&x'
}
yWz~WWÓÁ
YÓºz
¸
}
WW¡¢ÓÔy
m
¤Å
yW}£Õ
£y
yu¤l
}e|¦yu£§
yªO£W£{#{
Ñi
©{
OÑ yW}²"yu¤
°
(±e}Dy
¸
(
²
}'
Te&µ³uz({ª#
y
{ª
O
yW|~£Yi
¤¥
yu}£Õ
£y
ª
yyu¤
} yWz~¹
¯z
} z({
{i¼
º»
}
{YW£z~z({Y
$
}|&yW£
£y
§¼
»
}
{³Ö
iÑ
{
}
£{yW
}
\ §¶±e}Dy
(
¯²
}'ÂÃ
Ñ
yYz{
°
u}D
}|&yu£
£y
6`y
$|}Dy
z}
{
W£y Ñ ' » £ ¤¥ yu}£Õ £y yW¤_|¦yu£§ yªO£W×{O(W T{ª¶u u} {Y y D¬ {
´ W£yW}ªØyª4 &y Ù} {;z{#yu¤³ } yWz~£¹¯z } DZe}Dy ( ² } Ñ {'yu ¸
W T §$³&´Oµ³uz({ª# eµ6£{eª (y$£{Ô|(u}£Dz~£W}£§z{ ¤×z~l¤Åyu} ¤¥ yu}£Õ £y yW¤
{ W ~ |&yW£§ yªO£u£{Wii _ } ª y{lu} ~}DÚ §'yª'|W} Ñ ¶ª#y } ¤Å yW}£Õ £y
W£yu}(ª#{
"!
#
$%'&
()*
#
+,-.)(-0/1%&
#
+2
#
)34(%3657(%
#
+-+8
)"2:93- );< =8)939>?2
@
+ +ACB=%)(CDE-
F #
G2HAI)- 8=
#
%JK+) $ &
3+9C!
#
)):8 G):%-(%"L
M #
:NO PN N
9 #
Q%*?PR
#
)R)A A2
#
))
+-9TS)0Q%GPUGP
# S # )V
@
%N
9N(%WS
# #
Q%- < X)
#
S8)) $:N-$)T$JYAA
A:N3);N TZI)
-[\NAGL
]
M^L_1A F -"2H`"aAabc
MdPN;e
#
:N-93SA)=GPfSA g%ihA9T;j
#
%kT%)l%)m
#
) nSo&
;TS8 g%ih93)1N- -)e9TAp
#
Zqrse)Yj LCtSj)> )lS%uN:N)
@
%N)1S
#
LvD:wl/>L%xyLMz-{lSAA
@
1 )
@
)) :N # -)
Q%
#
#
Q%-)"2
@ N
# #
+A(9T:+dN-\N
#
G J
#
A)
#
3GP
# N-NlA)
Q%lS
#
:v
# ) ]
cE|} z1BEL%~lL%(%8L
M #
S9TKj>S
#
C);Cj
#
veL|}
]
`a u`AcLT >
#
>
`"Aa:9
#
)z)
#
z)A
# NN:j)d 9TNHHAeS8HS8)-}Q%GP
# N-N:Q%
#
)9T%
pX9T w9
#
(:N9
#
Q%LwM
#
S
#
IXBELH~lLi4(%8
]
`Aa
`"aAbc-2
#
l`"Aa2S
# #
)d iA
#
Pt
#
:N-9T})\):m
#
%'
;N)A+pLMz=9N9TA>w%(%-"2
#
))wN-T-M
#
?2
# NNX
#
))
S--%IS
#
e
#
A9T9>
#
Nl9
#
(:N9
#
Q%LC~
#
)lQ%3 )l-4(()=
MdL_m- F `aaAbl) 19nh93:)"O:%GAzGP1A"NN1
#
SL
1)9> fQpnI
#@#
Cv
#
)T|EA
#@#
$N(
#
SS:Nj
#
P
#
%
)39
#
(:N9
#
)l$qq
)Yj L
j
t0wA
#
))
#
w :GP
# S #
)$NNwN
S)1`"ALG5Ih93:>
@ # +
#
))89TS8
#
%HQ%: PHg% S:N:):%-)
5 # (:N9
#
Q%)lHLd%L}5
#
(?L28`"Ab-d+A1 )9N9TA)dev;L|EA G
BEL:~lL:%(p"L0t W-%
#
2l4(%8
# NNIN #
W93)>JYA)
w
`"AaIS
#
X5L\
#
%I5=A{1
#
%A"2z`"Aa-lSGLl`C=`"Aa`fS
#
=eLE_1%(
A
#
=:L%_1p(G2?`"a`2%SGL%p`L
vA)
#
A)zSN)%}-)H9N93)8S8e-%)HEveL-|} %dBEL~lL"%(%%&
-
#
)Q%E }:N @
SS93%H N-dE)d:N-)d
#
)H)d
#@#
l)Hqq s
dq qsd)Yj- )"LdM}
#@#
A}v
#
)?|}-A )H
# J # A)
#
[)dS8 g%ih93)
j
#
%kT%)1%-)-)"2?j
#
l-
#
))
#
28 1S-9TE
@ #
+1zj=AX
;9N(%l+dN:N
#
eS8m
#
:N-93SA)=GPfSA g%ihA9T1%1fS%
lS8 g%ih93)dN- )"LE
#
9N-(%
# NNl
@ N- eS
#
BEL~lL%(%8L
¡'¢?£¤¥Y¦^§o¨l©Yª-«o«¬©K¦G«o©"¤¥K¤¨¦"¤ ®ªm¯£°?±ª²z¤³:´¤H²o¤µ¦·¶"¸E¤¦K¤©K¥K¹¬§©Yº¼»"²o¬¨¦H´¯}¤¦Yª´¦?³:¤³E¹o©Y¤-»¯¤ ½¾
¿
§o´¨[½4À¾ÁoÂ
à ®
°3¯£¤Ä±¤«o¦Y´¬¨H²o¤¥©"¤Å4¤©K¤¨o±¤¥Æ§%£¬¨d¦K©Y¬-§oǤ²oª-¨o¥¯£Èo´¥Y¦K¬´©K¤²o¤¥³:ª¦KÈu¤³:ª¦K´Æ§"¤¥²o¤zÉ; ¢8ª¨¦K¬©
Ê
É1¬©Y´¦KËd¢8ª¨¦Y¬©»o½¾Ì-Íη»«%Âz½Ï"À^¤¦z²oª¨o¥z¯¤H¦K©Yª-´¦"¤ ÊÐ
¬-¨oª¯²:ÑGÂÒH¨"§o¦KÈ%»½¾-Ío½·Î·»o«%Â"Á-Ïo½Â
Ó ¤¦z«o©"¤¥Y¤¨"¦¤¤zªÇ¤±H«o¯§o¥²o¤H²z¤¦Kª´¯¥
# # # @
Q%))?d
#
)d
#
)z dA9
#
zm
#
¼JY9T oQ%
#
%11))?JYA93
#
S) m:N:-)
#
\N)1L
%J
#
H Qp:)
#
+A(93)G8
#
S>S )dkT
#
)2%}:SS8)E
#
&
#
93%HmN%)2%%eNN:
@
%N)d
#
)H -)dYj)E:N-)Ld )HS9T%
GPE
# J# )
#
A>GPTS8 g%ihA9T1j
#
%kT%):-p):%"h939T%
@
S #
: P%9N
#
:)
#
-)L
=N)9TA)E
#
(A + 1lQ%1)
#
)ESN-)%-
w
`aA28`"Alv D:A
`AaeM{2-9
#
G2%v;L%|}
`o%lv;L%|}
``m;L%|EA
`A`Am4(%8
`aaA`aaAb_1F
`A
#
)9
#
QWZ$]S6U^ XX X4S³[]\RWUÇfTVTRXYSi^
Mz)C
@ #
+A)w)w
# J # )
#
AW-)wSA gpHh9T-)6j
#
%kT--p)n-p)
#@#
%
|}-A %(p>)=A%%T+dN:N
#
9T-p;)>
#
-4((w);J
#
-)
:N #
-) Qp
#
#
Q%)L:
@
9T93%dSA )
@
)) \N #
):lS Kj93
) N) wzj-):Qp?PA
#
@ N[) -):
#
-)
#
A ):=S8 g%ih93lj
# J#
&
A)L} ):S%uN:N) SA:
@
:)
#
)=N
#
%::NY
#
A%)
#
39T -e
qr
)Kj- A2
@
LGHALd%Ld5
#
(GL2z`"Ab-2%SGLdbAb`"L
A
3&56< "!#%$'&)(+*,$-#/.1032546#/78*!:9;0=<>#?9
vD:
#
%S8)Nm9N(% )g%)N9
#
Q%:S8E
@
} )E
@
)): :N # -)
;Qp
#
#
Q%)[
#
);)AI
#
N@BAC?DFE8GIH:DJC?KMLON)PQC>R:H:A-SL1TFCUSe)
##
1vD:G2z`-L
V
@
X
#
)3w
@
==)-% "NXWHYC>PQR:HZPQD%C>[\PQHXWC>R:C]S[A_^;G uj
N
A>)1j+ )1S81
@
1 ):J
#
-)l?PwSA gpHh9T1 )>S )-)
%9TS -)"L
V
=SA
#
A Qpl
@ #
+1A-)S8$j
# # N
#
AX?PX-)mSo&
JY))N$S
#
fvD:S)$`"aAZnQ%[SASA)
#
wSN)-p
#
AN
P
#
(9NQ%:-1 P
#
+jL
M #
9N(%EEJ
#
-)
#
l-)dSA gpHh9T-)}j
#
)d-pOkT%)d%-)d:v DE&
A-SA)=)> PNT)e
# #
I3mN-)>);> PpS8
#
C)
SA gpHh9T-)}S
#
:mN--) )"L
1P)^>)dA )dQ%
# NNEJYNQ%939T%H )Nz)Qp?P
#
e:NE>qq
)Yj&
2
@
AzS )z A PS:dr
#
1-Gx
#
->| #
iM^Lr
#
T-:x
#
G2?`"A-
)f P NXn PpS8
#
$S
#
X1N)f)=S8=
# J# )
#
A)
SA gpHh9T-)"L
r&s rÌr6κr¦s r&s
ª³>¤¦KÈo¬²o¤i²o¤G¤z¦Y¬-¨l§o¦Y´¯´¥K¤H¯¤¥H¦Kª¹o¯¤ª§ ²o¤}²o´i¤©K¤¨o±¤¥¨o´¤¥ÂiÑ8¨l¤%¤¦»o¥Y´¼»8»X¥K¬¨¦
²o¤¥z¨o¬³E¹o©K¤¥8©"¤¤¯¥»¥Y¬´¤¨"¦
] ! " c # $
%
%
! " % &
('
# $ )
+*
)
+*
! ,)
-*
&
'
]
! " c # ] )
-*
! ! " )
-*
.&
c
# $ )
+*
% )
-*
)
-*
% )
-*
! " )
-*
&
% )
-*
&
'
# $ )
/*
)
/*
!
)
"*
&
'
ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ !
ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ
10
]
! " c # 3
] )0&
-*
! / )0&
-*
.&
0
c2
ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ ! ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ
ª:¥Y§o´¦K¤
0 ] 3! /
c
¤¥K¦54687!9;:2:<
=>?=@A(=
²%£¬©K²o©K¤CBz²o¤H¯ªE¥Y§o´¦K¤C 3 ! "
¤¦
"]
! " c2 ¼]
3! ! " c( ! "
0]
! " c2!
¤¥K¦z¯¤ED-6!FG4
=
6"HI7
=J 7!9K:(:<
=>?=/@?A(=J
²o¤d¯ª}¥K§o´¦K¤C ! ! " 8Â
LNM =@?
A 3 L 5Y8
A 8 A A
3&56<
vD:Z939T-l
#
SN)%
#
>)
#
9N(%;S
#
6NA;Cj-+ )"2
@ L
)
##
1vD:G2?`"aAb-SGLd%%pL$M
#
S9TKjX:N3
# 9 #
Yj3w
@
> )
@
))m?PX9>m-pS8)J4L}
#
)
#
)-; lN-
wPOOQ
CTFLSR:^LPQD%C>D.TH(U
L"V AXWHSBLR:[C>AYTHZDTHEZ\C>RZCUSCTH-H[VQLA D%[^\S TFH_S5ZC>R:C]SHZ^A-S SC>GV T]HS"UZH:GIH:^AHH:PQK-[AH5K-[\G\VQ[1STH-H(U
HZD]R:^^[P S[\^(V]_KZ[\PQPQH`R:^C^HT>T]H K-[PQD%C>H:PQPQH5R:^HTaRZ^H\Z\C>RZCUS H:^A K-[\G\VQ[1STH2bCZCUScVQ[1SH"de1TFL SH_TF[P
TFH_SfZ\C>GIH:PSC>[\PSIZHIR:^HTaRZ^^^PQHgZH SHS TFH:DJD%A H_S"U H:DBS^hSD%C>D%^;H"dS^K-K-HS-SC>R:HZG HZP8DiWL T]L
V T]LK-HNZ\H K-HZD%DJH TFH:DJD%A H2U DJA[C]SB[^^PV=TF^\S5jALP.Z PQ[G1hZAHNZ\H DJH:AG HS`ZH TFLkV A ["j\AH_SMSC>[\P
LAC?DFE8GlTH:DJCRZ^H:UGbUH`UzU
%
`GU
%
bmon D6C]T HZPATH_S^\TFD%HZALIL\^;D%LP8DZHBR:L1TFH:^A-SpZ\CqgTH:A H:PQDJH_S"U
RZ^HR:[^\SrTHZK:AC>AH/d LR:H-K TFH_SsZ\C>RZCUS H:^A-SlWL Kt[D.THSZ\HSD%HZA_GIH_SsZ\H TFL1V A ["jAHS-SC>[PYR:^C T]HS
L^A [\PQDV A[Z^C>D%HS"b Lu1L\PQD S[C?PvZ^/THZK:AC>AHIL\^\SMSCKME8LR:^HSZC?RZC]SH:^AIL\RZH-K^P SCwjP8H`VQ[1SCax
DJCy HZDB^P SCwj\PQHP`THjL\DJCy(m{z [GV L\AH"d T]HSZC?RZC]SH:^A-SsR:^C SHD%A [\^RZH:PQD`ZL\PS^PQHTFC|jPQH
LR:H-K"K-H:^}IZH_S L^DJAHS TFC|jPQH_S"U~VQ[^A R:[C>A S.^CUTSPQH`y[A_GIH:A L\C>HZP8D]VQL1S^PQHkV A ["j\AH_SMSC>[\P
LAC?DFE8GlTH:DJCRZ^HmIn DVQ[^AK-H_TFLGU KM[\GIG H:PQK-H/dVQLA TFH_S5V=TF^\Sy_[AD?S"UV [\^;AZH_SKMH:P.Z\A HL^}
V T]^SyLChT]HS"U)H:P S^;C?RZL\PQD6TFL GYtHZG HG LAK-EQH`R:^HBTFLV A[/j\A H_S-S C?[PL\AC>D]EQGlTHZD%CR:^H\,UGbUi`GU
U
%
`U
%
bm
Q
CK-HZD%D%H A H-KME8HZAKME8HIR:[^\S\y[^AP8C>D\RZ^H_TR:^HPV A["j\A H_SMSC>[\PvZ\[PQDT]HS DJH:AG HS
PQH8ZCq8WH:AH:PQDPRZ^H8Z~^^PQH^PQC>DTH2U5[^YR:^HTaRZ^H PQ[G1hZAH8RZ^C\ZC?RZC]SH TFL1V=TF^\SIEQL\^;D%H`V ^C]S"x
SLPQK-HZH TFLSR:^LPQD%C>D.TH\V A [V [ SCTH-H2UfTHZK:AC>R:H/d K-HZD%DJHV A[/j\AH_S-SC>[P8ZL\PSBTFHG tH:GIH [AZA HRZ^H
TFL1V A H:GICWHZAH(UV=TFL_K:LP8D K-EQLK:^PiZ\HSH_S D%H:AGIH_SlWLXK~t[\D.THZH TFLT]CwjP8HSZH_SSZC?RZC]SH:^A-SNR:^;C
T/^LsV A[Z^C>Db H:D TFH DJH:AG HRZ^CaU`ZL\PS K-H:DJD%H`V A ["jAHS-SC>[\PU ATH+V [\P.ZALXL^YDJH:AG HegZH T]L
DJAH LW TFL3RZ^H_T>TFH C]T LR:LC?DITH:D.TH S^hSD%C>DJ^PTH2Uy[\AGIH:A L ^PQHR:^LPQD%C>D.THIL\RZH-K TFL3RZ^H_T>TFH C]TyL\^Z\A L
DJH:PQD%HZA TFLSZ\C>R:C]SC>[P.m
#
) l)>[
#
)-w)T]L"G LP8C?WHZAHZH D%A[\^;R:H:ABTFH_SNZC?RZC]SH:^A-S: GA%&
)zjlS )-):S8 g%ih93)dS
#
- -):
# #
g%) )EJ
#
)
#
A)ESA)) )L
?? }S8 g%ih93
%
%
`">2"S
#
H%9TS A2" %()? )
@#
)#
%
`2
2:`>-l%l )e-p)
%
2d2;`8LwH)T dA); >
# # I)
@#
%
#@
1 ):
@
))S8)JY)E)
@#
)
#
) -)1) 9>)LG zSN)-p
#
)
m
# #
=)
@#
%
w
` `:b.E
`:b.:.: m
% ` ` `:b.:.1`- mb
H)l z)P
#
S-A Q%1 -)-9T-):l
#
Yjl- 1JY9T%ElSo&
+))A
#
(9NQ%d-}>:NdQ% ES8 g%ih93=1-)E>
@
)dQ%
P
#
J
#
)
%
b
w OO n PS^;C?DJH K-[G GIH T]HDJH:AG HT]H\V=TF^\S THT]HZR[TH P ^L
ZHZC>R:C]SHZ^AER:^H T/^^PQC?D.TH2U_H KME8HZAKME8HPV L\AGIC TFH_SNZC>R:C]SH:^;A SkR:^HTaRZ^HkV A["j\A H_SMSC>[\PIZ[\PQD
TFH_S5D%HZA_GIH_S5PQHZCq8WH:AH:PQDR:^HNZ^^PQHI^PQC?D.TH2U HZDR:^CaU HZP ZH_S K-H:P.ZL\PQDZH_SV T]^\SCy[\AD>SBL^}
V T]^S`yLChT]HS"UEZ\TH-K:A [CUSMSH:PQDK-[G G H"K-H:^}iZ\HTFL V A[/j\A H_S-S C?[P$`UGU
%
`mHPQHYDJA[^RZH
RZ^^^PQHV A ["j\AH_SMSC>[\PSZ\HK-HZD%DJH HS;VpWHMK-H2U K^H_SD8.UGUibmHV A H:P.Z1S`Z[\PQKBTFHBD%HZA_GIHmR:^;C
SH"D%A[\^RZHZLP STFL GYtH:GIH T]CwjP8HSR:^;H> ZH TFL V A H:G C?WHZAHPV A[/j\AH_S-S C?[PI`UHU
%
`UH TFH
[C?PS L]U6HZDHBD%HZP8DJHBT]LNZ\C>R:C]SC>[PkVW L\Aw,b HT>T]HBACTHZ^\S-SC>DU)H:D^[h:DJC?HZPSVQ[^APRZ^[D%C>H:PQD
%
bm
v-D:
#
@
)
#
+dN> >S Kj93eT
# J# )
#
An)eS8 g%ihA9T)>j
#
%k>&
%)H%)d
#
)G);+
#
lA)HGP
#
+jHJ
#
dj
# #
9>+H%m` }`aA
Q%GP
#
@
)
#
+dN;eS Yj-9TLMe9
#
%)l>A)
# N-N;\NS8)N>S
#
v DE&
AIS
#
%l P(
@
>`a u`ao3lS8T ;9 @BAC?DFE8GIH:DJC?K N)PQC>R:H:A-SL1TFCUS Ch-H:A
AC>G ^\SLH z)l
@
1
#
): -)"! L\DFE8HZG LD%C>K-L1T L"VQH:A-S
N
N):S
#
;L%~lLx()>)
##
mv D:AG2G`Ab-'L
?J
#
A1Q%;vD:C)"P
#
S8-1Qpe PpS8
#
3SA
#
1=j
#
)l
@
)-)1 \N # )ej
#
%kT%)m
#
A )1Q%H;)%1S
#
))[%)Ll
@
Q%: :SA gpHh9TE % %
b` = XbA
#
EJ
#
2E-9
#
Q%
Q%GP= 9> S
#
%GS
#
:
@
):lT%kT%:A9T
#
pHAT% C2
Q%G)3
@
)lj
#
%kT--p)%-)"L
#
):)w-) ]@
L?)
##
mv D:AG2G`Ab-'2%S?L}%c
#
)GQ%[
#
)B@BAC>D]EQG HZD%C>K-L
N)PQC?RZH:A-SL1T]C]S ]@
L;)
#A#
1vD:G2?`"aAb-2SGL pAc2v D:AnIN+
#
-9T%:
9N(%dS8zA
@
? )G
@
))GQ%
#
#
Q%)
w OOQ
^h_SDJC?DJ^H"d\ZL\PS T]LV A ["VQ[1STH:H(U
W
LBTFL V T]LK-H\ZH TFL TFH:DJD%A H2UR:^LD%AH [^ ^;PPV=TF^\SCj\A L\P.ZBPQ[G1hZAH\ZH D%HZA_GIH_SoZHT]L[V A ["j\AH_SMSC>[\P
Uib,Ud`UGU
%
`GU
%
b,U
%
\m T]LK-H/d DJ[\^\S
TFH_SZC>R:C]SHZ^A-S1ZH_SPQ[G1hZAHSR:^;C HZP ATHS^\TFD%HZA[PQDPZL\PS TFH_S G tH:GIH_SIT]Cwj\PQHSR:^;H T]HS
DJH:AG HSZHTFL[V A ["jAHS-SC>[P,bsTHT]HZR:H/d TFH_S DJH:AG HSZ\H TFL[V A ["jAHS-SC>[P L^1RZ^LA_ACTH(b G ^\TFD%CV T]C>H"d
K-HS`RZ^LA_ACTHSVQLAPRZ^H_TR:^HEZC>R:C]SH:^;A PQ^GlTH:ACR:^H`Z^D%H:AGIH T]HV=TF^\SYTH_TFH:RTH`ZH TFL1RZ^LP8DJC>DTH
#%$ Â Ê&
¥Yª-ª±~?¤-z¦K¬¨%»½4À('o½KÎp«%Â')»¬§¯£·¤²o´¦Y´¬-¨dÅ©Yª¨*±ª´¥K¤
Ê&
¥Kªª±G¤-z¦K¬¨%»A½ÍÌ)Ϋ%ÂÁÀÂ
[PQDACTHS^\TFDTH`ZHR:[1S S^2VVQ[1SC>D%C>[\PS"b A H:DJALPQK-EQH"de1T]HS HZP S ^C>D%H2U H:D8TH:KZA_C>RZH"dBK-HS S[\GIG HSBHZD
K-HSSZ\CqvTHZAHZP8KMH_SSZL\PS TFH GYtH:G H"[\A-Z\A HSR:^H TFH_S D%HZA_GIH_SsZ\H T]LV A H:GICWH:A HPV A ["jAHS-SC>[\Pb
KME8HZAKME8H/dD%[^D%HS TFH_SPV A ["j\AH_SMSC>[\PSNR:^CV H:^RZH:PQD SHA H:PQK-[P8DJAHZA1ZL\PSK-HS S[G GIH_SHZD
K-HS\ZCqgTH:A H:PQK-H_S/U H:P L1T?TFLP8D~ZH_S DJH:AG HSoZ^^PQH T]Cwj\PQHvWLBK-HZ^}1ZH TFL TFC|jPQHS^C>R:LPQD%Hm
Q
[C>DU
V L\A H/}\H:G\V=TFH2U
TFH DJH:AG H5Z~^^;P8HV A["jAHS-SC>[\PNZ\H5K-H:DJD%H H_S;VpWH:K-H5R:^;C=SHBD%A [^R:H5Z\LPS T]L
GYtH:G HTFCwj\PQH\R:^;HT]H DJH:AG HiZHT]LV AH:GICWHZAH]V A["jAHS-SC>[P,b S[C?D
TFL`Z\CqvTHZAHZP8KMH\R:^^[P
[h:DJC?HZPQD H:P A H:DJALPQK-EQL\PQD
Z^ DJH:AG H C?GIGlTH!Z\C>LD%H:GIH:PQD8S ^2VNTHZAC?HZ^ARZ^CSH D%A [^R:H\ZL\PS
TFLG tH:GIH TFCwj\PQH5R:^H TFH D%H:AGIH:`ZH T]LV AHZG CWH:A HV A ["jAHS-SC>[P,b S [\C>D H:P P ^PSZ\C>RZCUS H:^A
PQ^GlTH:ACR:^HIZ^ D%H:AGIH T]H`V T]^\S H_TFH:RTT H2U5H:D TFL TFH:D%DJAHSZH T]LvR:^LPQD%C>D.THEV A[V [ SCTH:H2bIL1T][A-S
SH:A L ^PgZC>R:C]SHZ^A`R:^C^C]TyL^Z\A LH_S-SLu1H:A(m
GA)zj-lA9T93:S93}-p-9TS
% %
<`b
%
p#<\
d
@
2oS
#
H:9N-(%2 >b
%
b
%
> 939TH
@
))iS8)) )
- :Q%
OO
T]L ATHZ^KZD%C>[\PXATH:^S-SC>D V [\^A5K-EQL\KZ^PYZ\HSEZH:^} }L
L
A
1
JlJlAA 1O7
8 A A 3&56<
Mz)EAp9TS8
#
)H:v D:A>%eNN @ @
9T%?%N))N):S
#
H)EN)
#
)Ed )
%1))
#
g}N>e-9TS> lSpzN:NTlJ
#
A)
#
f>vD:C1>A
):)
#
)1>
#
j+A >Q%:N-eS
#
l Le
#
9THfIS8le/>L8xL
Mz{A28L 9
#
G28veLz|E
]
c2z[S )1
#
6;Lz|E HlS)lBELz~lL
%(%-"L
r
Ê
C
Mz{
#
S NEEN-)3GP@BAC>D]EQG HZD%C>K-L N6PQC>R:HZA S L TFC]Sz
#
) @ K:D%L5n A^ZC?DJ[\A^Ge2
v
@
9>A2d`"Aa2SGL>`" AbL[ d-S P%9TS lnS8 g%ih93 8
%
`$
1
# #
3lv D:A
#
)zQ%1
# J # )
#
ATl-lSA gpHh9TAL
Mz-{2zQ%dGPN
#
S
#
)l)
#
)'J
#
S
#
1
#
9N(pl>v-D:?2GCA>
#
3
#
)[)
# #
))NIj
# # F
9
#
CTw%-S9>w`"Aa"L=E
=%-p[T3p N
OO
!YHZD]EQ[Z^\SjH:PQH:AL1T]C]S C>PQR:HSD%CwjL\P.ZZ\C`ZC>R:C]S[AHS
y[A_GI^\TFL\A^G ALD%C>[PQL TFC>^G C>PQD%HKj\AL TFC>^G H"}1ZLD%C]S\ZC>R:C]S[A_ChZ^\S PQ^GIH:A [\A^G3A LD%C>[\PQL1T]^;G
C>PQD%HjA[A^Gom
d)> >
#
)l);S8 g%ih93)>+NT=lA)zj-T-9T931%9TS ;
#
J# -)
#
;eS8 g%ihA9Tdb
T
Ta
T T TEQ%GP A;LG (-(
J
#
A)
#
>3TS%EGPTS8 g%ih93}-Q% !
#@
CSA g%ihA9T1Q%
#
#
Qp#" %$ '& ?L1 i(A)C%#(fS )1+
#
wQ%
)l%z%);CSA g%ihA9T>j
# J #
-)1l9
#
Q%;Q%e
#3@#
C
@
)
TS8 g%ihA9T)<*(3)}3
@
)E
#1@#
d3SA gpHh9T1j
# J #
A)-}=
SApL
?H :S8 g%ih93}bX Xa X ==E S+(S#`1dA%H
#
@#
EbaAALzH) AJYA9TE>
# #
e-)d
@
))d-:9>2o>N
,%$ Â Ê-
¬¦K¦·Å©Y´¤²/.3´¯Èo¤¯³
¤´¹o¨o´Ë-»o½Í10¾'Ϋ%ÂÏ-Ï10¶"ÏÏ-¾oÂ