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I have to prove Bezout's Lemma.

I have proven that since gcd (a, b) divides a and gcd (a, b) divides b, gcd (a, b) divides sa + tb.

I've made use of the well-ordering principle and Euclid's Algorithm to show that sa + tb divides a and sa + tb divides b.

What I can't prove is that sa + tb divides gcd (a, b).

Please help me here.

Thank you.