The fourth known primitive solution to $a^5 + b^5 + c^5 + d^5 = e^5$
Number Theory
2026-04-22 v2
Abstract
We report the fourth known primitive solution to the Diophantine equation , extending the list of solutions from 1966, 1996, and 2004. This result was obtained via a large-scale computational search based on an optimized meet-in-the-middle strategy. We describe the search algorithm, the techniques enabling it at scale, and the computational ranges explored.
Keywords
Cite
@article{arxiv.2603.05549,
title = {The fourth known primitive solution to $a^5 + b^5 + c^5 + d^5 = e^5$},
author = {Jeffrey Braun},
journal= {arXiv preprint arXiv:2603.05549},
year = {2026}
}
Comments
Expanded and clarified the search algorithm, implementation details, and computational results