An algorithm for the Product-Sum Equality
Number Theory
2025-08-14 v1
Abstract
We propose a recursive algorithm for identifying all finite sequences of positive integers whose product equals their sum. Our method uses solutions of strictly shorter length that are iteratively extended in pursuit of a valid solution. The algorithm is efficient, with a time complexity similar to the quick sort algorithm.
Cite
@article{arxiv.2508.09647,
title = {An algorithm for the Product-Sum Equality},
author = {Hlib Husarov and Eberhard Mayerhofer},
journal= {arXiv preprint arXiv:2508.09647},
year = {2025}
}
Comments
13 pages, 1 Table