2014•viXraRequires access

The Strong Finiteness of Fermat, Double Fermat and Catalan-type Fermat Primes

Pingyuan Zhou

Abstract

Abstract: In this paper we present that so-called double Fermat numbers are an infinite subset of well-known Fermat numbers and so-called Catalan-type Fermat numbers are also an infinite subset of Fermat numbers as well as double Fermat primes and Catalan-type Fermat primes are all strongly finite as Fermat primes do. From it we get the same result that composite Fermat numbers, composite double Fermat numbers and composite Catalan-type Fermat numbers are all infinite.

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Key concepts: Fermat number, Wieferich prime, Fermat's little theorem, Fermat's Last Theorem, Mathematics, Fermat's theorem on sums of two squares, Regular prime, Catalan number