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

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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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_ilsegugio_

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Nice video! But please, just a couple more examples! I figured out that for the integers 56 and 32, 56x + 32y = 8, if x = -1 and y = 2. But I'm not sure how I did it! I mean I sort of get the algorithm, but there was some guessing and checking going on along the way. So I'm still not 100% comfortable with the algorithm. PLEASE just a couple more examples!!!! If you do, I promise to buy you a beer, coffee, or any beverage you like!

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ganeshgajavelli

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