fw刚学数论，求证：

$gcd(x,y)=gcd(x-y,y)$

证明：

设 $gcd(x,y)=a$

$\therefore a \mid x$ , $\therefore a \mid y$

$\therefore a \mid x-y$

$\therefore gcd(x,y)=gcd(x-y,y)$

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