Diophantine equations for integers.
Diophantine equations for integers.
Diophantine equations for integers.
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Theorem 1For any nonzero <strong>integers</strong> a and b, thereexist <strong>integers</strong> x* and y* such thatgcd(a,b) ax* + by*.(Proof <strong>for</strong> Math 133!)When you have a linear <strong>Diophantine</strong> equation to solve,the first question you should ask about that <strong>Diophantine</strong>equation is whether or not the equation admits solutionsin <strong>integers</strong>.The following theorem tells you how to find the answer tothis question.
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