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Large solutions of small equations

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The fact that the smallest solution of a Diophantine equation can often be quite large relative to the size of the equation has been a source of bafflement—and delight—for number theorists since at least the time of Fermat. It remains one of the least well understood phenomena in the study of Diophantine equations. I will discuss a few equations, like the Fermat-Pell equation, and elliptic curves, in which some (still very limited) theoretical understanding has been achieved.

This talk is part of the Kuwait Foundation Lectures series.

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