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arXiv · 2508.09647

An algorithm for the Product-Sum Equality

Hlib Husarov·Eberhard Mayerhofer
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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.

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Hlib Husarov, Eberhard Mayerhofer. 2025-08-13. An algorithm for the Product-Sum Equality. https://arxiv.org/abs/2508.09647

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