 Fermat pseudoprime

An odd composite number $N$ is a Fermat pseudoprime to a coprime base $b$ when

A Fermat pseudoprime is relative to its base. For example, $341=11\cdot 31$ passes base $2$, but base $3$ yields $3^{340}\equiv 56(\mathrm{mod}341)$, a Fermat witness. A Carmichael number has the stronger all-coprime-base property. This explains why finding one deceptive base and proving universal deception require different arguments.