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arXiv · 2506.01099

On one of Erd\H{o}s' Problems -- An Efficient Search for Benelux Pairs

Christian Hercher
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Abstract

Erd\H{o}s asked for positive integers $m 2^{40}$. For the analogous problem of integers $m<n$ with $m$ and $n+1$ having the same set of prime factors and $m+1$ and $n$having the same set of prime factors, the situation is very similar: An infinite series and one exceptional solution with $n\leq 2^{22}+2^{12}\approx 4.2\cdot 10^6$ were known. We prove that there are no other exceptional solutions with $n<1.4\cdot 10^{12}$.

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Christian Hercher. 2025-06-01. On one of Erd\H{o}s' Problems -- An Efficient Search for Benelux Pairs. https://arxiv.org/abs/2506.01099

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