Journal of Integer Sequences, Vol. 25 (2022), Article 22.3.1

Equal Sums of Two Distinct Like Powers

Samuel S. Wagstaff, Jr.
Center for Education and Research in Information Assurance and Security, and Department of Computer Sciences
Purdue University
West Lafayette, IN 47907-1398


We study the equation aj + bj = ck + dk for positive integers a, b, c, d, and 2 < j < k. Two heuristic arguments correctly predict the cases in which the equation has primitive solutions.

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(Concerned with sequences A003336 A003347 A003358 A004999.)

Received January 8 2022; revised version received February 24 2022; March 6 2022. Published in Journal of Integer Sequences, March 6 2022.

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