The fourth known primitive solution to $a^5 + b^5 + c^5 + d^5 = e^5$

Abstract

We report the fourth known primitive solution to the Diophantine equation $a^5 + b^5 + c^5 + d^5 = e^5$, 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.