Diophantine equations for integers.
Diophantine equations for integers.
Diophantine equations for integers.
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Theorem 4If gcd(a,b)│c, then the linear <strong>Diophantine</strong>equation ax + by c has a solution.Proof: Let d gcd(a,b). Since d|c, dp c<strong>for</strong> some integer p.By Theorem 1, there are <strong>integers</strong> x* and y*such that d ax* + by*.So c dp a(x*p) + b(y*p).Hence ax + by c has a solution, namelyx o x*p and y o y*p.
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