Information about diophantine equation

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Reference no: EM13124585

Let R be a PID. Consider the Diophantine equation ax+by=N where a,b and N are integers and a,b are nonzero. Suppose x_0, y_0 is a solution: ax_0+by_0=N. Prove that the full set of solutions to this equation is given by

x = x_0 + (mb/gcd(a,b))

y = y_0 - (ma/gcd(a,b))

as m ranges over the integers.

Reference no: EM13124585

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