Fermat Numbers: Pseudoprimality and Primality Constraints
Abstract
We establish a necessary condition for pseudoprimality and a sufficient condition for primality of Fermat numbers, based on a congruence involving the exponent (Fn-1)/4. Moreover, in connection with P\'epin's primality test, we obtain a characterization of pseudoprimality to the base 3 (and, more generally, to other P\'epin-admissible bases).
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