Difference between revisions of "2011 PuMAC Problems/NT Problem A8"
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Latest revision as of 16:30, 22 June 2020
By multiplying both sides by 2 and simplifying, the condition becomes . This is a variant of Pell's Equation with minimal solution . We can obtain all solutions by computing
In particular, we get , , and . This third solution corresponds to . Indeed, is the third consecutive Pythagorean triple.