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

TL;DR

This paper presents the discovery of the fourth primitive solution to the fifth power sum Diophantine equation, achieved through large-scale computational search and optimized algorithms.

Contribution

It reports the first new primitive solution since 2004, using advanced meet-in-the-middle techniques and extensive computational exploration.

Findings

Identified the fourth primitive solution to the equation.

Developed an optimized meet-in-the-middle search algorithm.

Explored large computational ranges to find solutions.

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.