A Pépin-Type Characterization for Fermat Pseudoprimes
Year: 2026
Type: preprint
Abstract: Pépin'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 Pépin'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 $3$.
Source: arXiv (Cornell University)
Author: Starni, Paolo
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7158794643
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