Two dimensional covering systems and possible prime producing $a^m-b^n$

Andrew Granville; Francesco Pappalardi

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arXiv · 2601.10296

Two dimensional covering systems and possible prime producing $a^m-b^n$

Andrew Granville·Francesco Pappalardi

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Abstract

We exhibit a new application of two dimensional covering systems, examples of integer pairs $a,b$ for which $a^m-b^n$ has a prime divisor from some given finite set of primes, for every pair of integers $m,n\geq 0$. This leads us to conjecture what are the only possible obstructions to $|a^m-b^n|$ taking on infinitely many distinct prime values.

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Andrew Granville, Francesco Pappalardi. 2026-04-11. Two dimensional covering systems and possible prime producing $a^m-b^n$. https://arxiv.org/abs/2601.10296

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