Page 74 - Numbertheory

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232 + 1 ()

641 ( ) 257 ( ) 101 ( ) 97 ( )

641 = 24 + 54 = 5× 27 +1 :( )

232 = 24 × 228

= (641− 54 ) × 228
= 641× 228 − 54 × 228
= 641× 228 − (5× 27 )4
= 641× 228 − (641−1)4

. m (641−1)4 = 641m +1

232 = 641× 228 − 641m −1 641

= 641(228 − m ) −1

. 232 +1

gcd(a, b ) = 1 cba ( )

gcd(a, c ) c a +b

c() a( ) 2( ) 1 ()

.d a d c gcd(a, c ) = d : ()
.d b
. d | a d  (a + b ) c  (a + b )
.d =1
gcd(a, b ) = 1

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