Peshu theorem (or Bezu theorem) is named after the French mathematician Etienne Peshu. Explain that for any integer A, B and its greatest common divisor D, the linear indefinite equation about the unknown number X, Y (called Peishu equation): If A and B are integers and gcd(a, b)=d, then for any integer X, Y, ax+by must be a multiple of D.

One of its important corollaries is that A and B are coprime if and only if there is an integer X, and Y makes ax+by= 1.

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If a and b are coprime, then there is an integer x, y, so ax+by= 1. Multiply both sides by c and you will get the solution.

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