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arXiv · 2507.03727

Egyptian fractions for few primes

Agustina Czenky·Emily McGovern·Julia Plavnik·Eric Rowell·Abigail Watkins
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Abstract

We study solutions to the Egyptian fractions equation with the prime factors of the denominators constrained to lie in a fixed set of primes. We evaluate the effectiveness of the greedy algorithm in establishing bounds on such solutions. Additionally, we present improved algorithms for generating low-rank solutions and solutions restricted to specific prime sets. Computational results obtained using these algorithms are provided, alongside a discussion on their performance.

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Agustina Czenky, Emily McGovern, Julia Plavnik, Eric Rowell, Abigail Watkins. 2025-07-04. Egyptian fractions for few primes. https://arxiv.org/abs/2507.03727

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