Introduction

Abstract

The French mathematician Pierre de Fermat (1601–1665) became well known not only due to Fermat’s last theorem (proved in [Wiles] and [Taylor, Wiles]) and Fermat’s little theorem (proved by Euler), but also due to the conjecture that all the numbers

EquationSource% MathType!MTEF!2!1!+- % feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaGaamOramaaBa % aaleaacaWGTbaabeaakiabg2da9iaaikdadaahaaWcbeqaaiaaikda % daahaaadbeqaaiaad2gaaaaaaOGaey4kaSIaaGymaiaaywW7caWGMb % Gaam4BaiaadkhacaaMc8UaamyBaiabg2da9iaaicdacaGGSaGaaGym % aiaacYcacaaIYaGaaiilaiablAcilbaa!4A9D!EquationSource$$ [\[{F_m} = {2^{{2^m}}} + 1\quad for\,m = 0,1,2, \ldots \ $$

((1.1))

are prime. The numbers F _m are called Fermat numbers after him.

Mathematics is the queen of the sciences and arithmetic the queen of mathematics

Carl Friedrich Gauss