Page 47 - Numbertheory
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18 ( ) : 198 252 6( ) ()
9( ) 3 ()
: .( )
252 = 1×198 + 54
198 = 3×54 + 36
54 = 1× 36 +18
36 = 2×18 + 0
. gcd(198, 252) = 18
()
a + b = 500 ba ()
. gcd(a,b ) = 7
.a gcd(a, a +1) = 1 ( )
.a gcd(a, a − 2) = 1 ( )
2 (a2 + a) ( )
.a
gcd(a, b ) = 7 a + b = 500 ()
. 7 500 . 7 (a + b ) 7 a 7 b
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