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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.

Keywords

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