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The Hardy-Littlewood circle method and Waring's problem

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The Hardy-Littlewood circle method provides a framework for solving a number of problems in number theory. One of these is Waring’s problem: for any integer k that is at least 2, there is some s=s(k) such that any sufficiently large positive integer can be expressed as the sum of s kth powers. I shall describe the ideas of the method, by showing how they can be used to solve Waring’s problem.

This talk is part of the Junior Algebra/Logic/Number Theory seminar series.

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