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Variations on Fermat: an agony in four fits

Fermat’s Last Theorem has been a source of fascination and the motivation for an enormous amount of mathematics over the last few centuries, both in attempts (eventually successful) to prove it and as the inspiration for other related questions.

This is the story of how an algebraic question inspired by Fermat’s Last Theorem morphed into an analytic question, which subsequently turned out to be expressed best as a geometric question, which could be answered using basic methods of plane geometry.

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