Diophantine Equation: ax+by=gcd(a,b) ← Number Theory

Once you know how to solve diophantine equations with a single variable, the next step in complexity is to consider equations with two variables.  The simplest such equations are linear and take the form ax+by=c.  Before we solve this equation generally, we need a preliminary result.  We show that you can solve the equation ax+by=GCD(a,b) by performing the Euclidean algorithm, and then reverse-substituting to arrive at a single solution.

Teacher: Michael Harrison

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