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Answers for “我们能通过算法找到系数 x 和 y 吗?”

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The converse states that if integers a and b are coprime (i.e., their greatest common divisor is 1), then there exist integer coefficients x and y such that ax+by=1. This is provided by Bézout's identity.

Conditions: a and b are coprime integers.; gcd(a,b) = 1.