HDU 5974 A Simple Math Problem ——（数论，大连区域赛）

　　给大一的排位赛中数论的一题。好吧不会做...提供一个题解吧：http://blog.csdn.net/aozil_yang/article/details/53538854。

　　又学了一个新的公式..如果x和y互质，那么x+y和x*y互质。证明如下：随便找一个x中有的因子c，因为x，y互质，因此c不是y的因子。同时c是x*y的因子，由同余模方程知（x+y）% c = x % c + y % c = 0 + y % c。因为c不是y的因子，所以不等于0，所以c不是x+y的因子。同理可以证得x和y中的所有因子都不是x+y的因子，却都是x*y的因子，即x+y和x*y没有公共的因子，因此它们互质。

时间： 2024-11-29 01:25:09

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