下题1中，用到了这个知识点。 80. 7589-!-item-!-187;#058&005492 If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y ?
是不是这样啊 1） x=12u then 12u=8y+12 then 3u=2y+3 then y=3(u-1)/2 coz y is integer, then u-1 is muliple of 2, if u =3, then x=36, y= 3, gcd=3, if u=5, then x=60, y = 6, gcd=6, so insufficient
2) y=12z, x=8*12z+12= 12(8z+1) coz the gcd of z and 8z+1 is 1 ( if gcd is not 1, then (8z+1)/z should be integer, but this number cannot be integer), so the gcd of x and y is 12, so B
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发表于 2010-6-9 10:25:08
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