Number Theory

    

Diophantine Quadruples and Ideal Solutions of the Prouhet–Tarry–Escott Problem of Size Four

Authors: Philip Gibbs

A rational Diophantine m-tuple is a set of m rational numbers such that the product of any two is one less than a square. The Prouhet-Tarry-Escott problem seeks two different multisets of n integers such that the sums of like powers of each set are equal for all exponents up to some k < n. Here a new connection is established between rational Diophantine quadruples (m=4) and ideal solutions of the Prouhet–Tarry–Escott problem of size 4 (n=4, k=3) Both problems are shown to be related to finding 3 by 3 singular matrices of integers whose 9 elements are all square.

Comments: 8 Pages.

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[v1] 2021-09-16 06:51:33

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