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pbïšbî‹Üa@ò†b¾@ð€jî‹vnÜa@çbznàfia@|ïz—m pbïšbî‹Üa@ò†b¾@ð€jî‹vnÜa@çbznàfia@|ïz—m pbïšbî‹Üa@ò†b¾@ð€jî‹vnÜa@çbznàfia@|ïz—m pbïšbî‹Üa@ò†b¾@ð€jî‹vnÜa@çbznàfia@|ïz—m

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pbïšbî‹Üa@ò†b¾@ð€jî‹vnÜa@çbznàfia@|ïz—m pbïšbî‹Üa@ò†b¾@ð€jî‹vnÜa@çbznàfia@|ïz—m pbïšbî‹Üa@ò†b¾@ð€jî‹vnÜa@çbznàfia@|ïz—m pbïšbî‹Üa@ò†b¾@ð€jî‹vnÜa@çbznàfia@|ïz—m

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@ðÝî@b·@Ӌɾa@Τ Z

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[ ] [ ] [ ]

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=           =    + −  =    + +     + −  =    + +    −    + +    =      + 

(3 À@ÞzåÜ @ó܆bɾa@

Ε

@Z 2

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2 1 2 2 2 2

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= −    + +   +    ⇔   =   +      +  + = + ⇔ − ( ) ( ) ( ) ( ) ( { ) ( ) }

2 2 2

1 1 0 1 1 , 1, 0 ; 1, 0 0 0 x y y x y x y y x y x y y x y    + =   ⇔    + +  =  =      +  + = =   ⇔  ⇔  ⇔ ∈ − = =  

@ @ @ó܆bɾa@çhÐ@êåà@ì @Z 2

X = Ι

2 À@µÝy@ÞjÕm@L@ @báè@

Ε ( ) 1, 0

2@Z

M = Ι ( 1, 0 )

2ì@

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N@ @ @

•••• @âÔŠ@æî‹ánÜa @âÔŠ@æî‹ánÜa @âÔŠ@æî‹ánÜa @âÔŠ@æî‹ánÜa ZZZZ 02

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{ } 1

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a ∈ −

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1 a =

çhÐ@L@ ëØ‹à@Ö¨@çaŠì†@

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@íè@

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z iz i

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C

N@

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@âÔŠ@æî‹ánÜa ••••

@âÔŠ@æî‹ánÜa @âÔŠ@æî‹ánÜa

@âÔŠ@æî‹ánÜa ZZZZ 03

À@nÉä

×

ℤ ℤ

¾a@

@ó܆bÉ

( ) Ε : 28 x 15 y = − 6

@Z N@

(1

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@ @

28 3 15 6 × − × = 84 90 − = − 6

@ @@ó܆bÉáÝÜ@™b‚@Þy@

( ) 3, 6

@xìÜa@L@çˆg

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N@

ÞÙÜ@

( ) x y ,

×

æà@

ℤ ℤ

@båî‡Ü@L@

Z

( )

@ @

( ) ( )

28 15 28 3 15 6

28 3 15 6

x y

x y

Ε ⇔ − = × − ×

⇔ − = −

@çˆg

( )

Z@

15 / 28 x − 3

@

@ @

@çc@b·@ì

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15 ∧ 28 1 =

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( )

@Z

15 / x − 3

N@

@ @

@çhÐ@êåà@ì Z

@ @

@

( ) ( )

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( )

15 / 3

28 3 15 6

/ 3 15

28 15 15 6

/ 3 15

6 28

x

x y

x k

k k y

x k

k y k

 − Ε ⇔ 

− = −



− =

⇔ ∃ ∈  

× = −

= +

⇔ ∃ ∈  

 = +

@ @

@ðÜbnÜbi@ì

( )

@Z

{ 3 15 , 6 28 / }

S = + k + k k

ℤ N@

@ @

(2

À@Þz€ä

@óáÅåÜa@ℤ

( ) [ ]

@Z

[ ]

: 8 28 2 15 S z

z

 ≡

 

 ≡

N@

@ @

ÞÙÜ æà@

z

@båî‡Ü@L@ℤ Z

( ) ( )

( ) ( )

2

28 / 8 8 28

, /

2 15

15 / 2

z z

S z z

α β α

β

  − =

⇔   ⇔ ∃ ∈ 

−  − =



@ @ ℤ

@çˆg

( z − − − = 8 ) ( z 2 ) 28 α 15 β

@Z

@

@ @

@çc@ôåÉá€i

@Z

28 α − 15 β = − 6

@ @

(5)

@çˆg

( α β , ) ( = + 3 15 , 6 k + 28 k ) / k

@Z

@ @

@êåà@ì

( )

@Z

8 28 3 15 /

z − = + k k

@ @

@ñc

@Z

92 420 /

z = + k k

@ @

@çbØ@aˆg@L@bïÙÈ

@Z

92 420

z = + k

@sïy@

k

ℤ N@

@çhÐ

( )

@Z

8 28 3 15

z − = − k

( )

@ì@

2 15 6 28

z − = − k

@ @

@çˆg

[ ]

@Z

[ ]

8 28 2 15 z

z

 ≡

 

 ≡

N@

@ @

óáÅåÜa@ßíÝy@óÈíáváÐ@L@ðÜbnÜbi@ì

( ) S

À@

@ðè@ℤ

{ 92 420 / }

@Z

S = + k k

ℤ N@

@ @

(3

@óïåàÜa@ò‡¾a@ßþ‚@çíÙî@öa‹Ñ—Üa@òŠb’fia@tbÉjäg

@I

@óÕïÔ‡Übi

@H

@ÞïÝÜa@Ò—nåà@æà@bÔþXäg I

@@H

0h

@

2 28 d

J

= + α

@sïy@L@

α ∈

ℕ N@

@ @

@óïåàÜa@ò‡¾a@ßþ‚@çíÙî@öa‹á¨a@òŠb’fia@tbÉjäg@ì

@Z

R

8 15 d = + β

@sïy@L@

β ∈

ℕ N@

@ @

m

@óïåàÜa@ò‡¾a@ßþ‚@bÉà@µmŠb’fia@tbÉjäg@ÖibXn

@Z

J R

d = d = d

N@

@çc@ñc

@Z

@óáÅåÜa@Þy@íè@

d

[ ]

@Z

[ ]

8 28 2 15 d

d

 ≡

 

 ≡

@óÈíáa@À@

N@ℕ

@ @

@ßaüÜa@óvïnä@ßbáÉnŽbi (2

@çc@wnånä@L Z@

92 420 / d = + k k

ℕ N@

@ @

@ðè@bÉà@µmŠb’fia@béïÐ@ÖibXnm@óïåàŒ@ò‡à@‹Í–c

@Z

92 min d =

@ @

@„îŠbnÜa@paˆ@óÅzÝÜa@À@Ú܈@ì

1

1 32 min

@Z

t = h

N@

@ @

_@ò‹à@ðäbrÜ@µnï÷í›Üa@µmŠb’fia@tbÉjäg@béïÐ@ÖibXnnŽ@ð€nÜa@óÅzÝÜa@„îŠbm@íè@bà

@ @

@ @

@ @

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