New results in equal sums of like powers

Ekl, Randy

doi:10.1090/S0025-5718-98-00979-X

New results in equal sums of like powers
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by Randy L. Ekl PDF

Math. Comp. 67 (1998), 1309-1315 Request permission

Abstract:

This paper reports on new results for the equation \begin{equation*}\sum _{i=1}^{m} a_{i}^{k}=\sum _{j=1}^{n} b_{j}^{k},\end{equation*} i.e., equal sums of like powers. Since the 1967 Lander, Parkin and Selfridge survey paper [A Survey of Equal Sums of Like Powers, Mathematics of Computation 21 (1967), 446–459], few other numeric results have been published (see Elkies [On $A^{4}+B^{4}+C^{4} = D^{4}$, Mathematics of Computation 51 (1988), 825-835] and Ekl [Equal Sums of Four Seventh Powers, Mathematics of Computation 65 (1996), 1755-1756]). The present paper reports on several new smallest primitive solutions. Further, search limits have been extended in many cases, and tables of solutions are presented. Additionally, new solutions to the same class of problems in distinct integers have been discovered.

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