Page 50 - Numbertheory

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ba

. gcd(a,b ) = 1

ba

.d . a −b a +b

. d b d a . gcd(d , 2) = 1

. d =1 . gcd(a, b ) = 1

. a +b a −b ba

d  2b d 2a .d = 2e d

.d = 2 e =1 . e b e a

y x ()

x +y
30 36

. 1 ( ) 1 ( ) 1 ( ) 1 ()
180 90 36 30

. x +y =z :( )
30 36 . 36x + 30y = (30× 36)z

z

36x + 30y

. gcd(36, 30) = 6 36x + 30y

. 6 =1 x +y
30 × 36 180 30 36

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