Pei is a theorem and Euclidean algorithm to expand

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Pei is a Theorem

Shu Pei Theorem (or Bezu theorem) is named after the French mathematician Etienne Shu Pei, whose form can be expressed as:

For \ (\ FORALL A, B \ in the Z _ + \) , provided \ (d = gcd (a, b) \)

Then there is \ (x, y \ in Z _ + \) such that: \ (D = AX by + \)

prove:

由于 \(d\mid a,d\mid b\) 则 \(d\mid ax,d\mid by\) 因此 \(d\mid (ax+by)\) 故 \(ax+by=k\cdot d,k\in Z\)