RT，推导过程是这样吗？

$ax+by=c,\gcd(a,b)|c$

$c=k\times\gcd(a,b)$

$a(kx)+b(ky)=k\times\gcd(a,b)=c$

$ax_{1}+by_{1}=\gcd(a,b)=\gcd(b,a \mod b) = bx_{2}+(a \mod b)\times y_{2}$

$ax_{1}+by_{1}=bx_{2}+[(a \mod b)\times y_{2}]=bx_{2}+(a-a\div b\times b)\times y_{2}=ay_{2}+b(x_{2}-a\div b \times y_{2})$

结论：

$x=y_{2}$

$y=x_{2}-a\div b \times y_{2}$