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arXiv · 2604.25973

A P\'epin-Type Characterization for Fermat Pseudoprimes

Paolo Starni
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Abstract

P\'epin's primality test asserts that, for $n\ge2$, \[ 3^{(F_n-1)/2}\equiv -1 \pmod{F_n} \] if and only if $F_n$ is prime. We establish a natural analogue of P\'epin's criterion for pseudoprimality. More precisely, we prove that, for \mbox{$n\ge5$,} \[ 3^{(F_n-1)/2}\equiv 1 \pmod{F_n} \] if and only if $F_n$ is pseudoprime to the base $3$.

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Paolo Starni. 2026-04-28. A P\'epin-Type Characterization for Fermat Pseudoprimes. https://arxiv.org/abs/2604.25973

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