Perfect powers expressible as sums of two fifth or seventh powers

S.R. Dahmen, S. Siksek

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

We show that the generalized Fermat equations with signatures (5, 5, 7), (5, 5, 19), and (7, 7, 5)(and unit coefficients) have no non-trivial primitive integer solutions. Assuming GRH, we also prove the non-existence of non-trivial primitive integer solutions for the signatures (5, 5, 11), (5, 5, 13), and (7, 7, 11). The main ingredients for obtaining our results are descent techniques, the method of Chabauty-Coleman, and the modular approach to Diophantine equations.
Original languageEnglish
Pages (from-to)65-100
Number of pages36
JournalActa Arithmetica
Volume164
Issue number1
DOIs
Publication statusPublished - 2014

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