Pierre de Fermat had first stated the theorem known as Fermat’s Little Theorem, the basis for the Fermat primality test and one of the fundamental results of elementary number theory, in a letter dated October 18, 1640, to his friend and confidant Frénicle de Bessy as the following: p divides a p−1 − 1 whenever p is prime and a is coprime to p. As usual, Fermat did not prove his assertion, only stating: Et cette proposition est généralement vraie en toutes progressions et en tous nombres premiers; de quoi je vous envoierois la démonstration, si je n'appréhendois d'être trop long. (And this proposition is generally true for all progressions and for all prime numbers; the proof of which I would send to you, if I were not afraid to be too long.)

Euler first publishes a proof in 1736 in a paper entitled "Theorematum Quorundam ad Numeros Primos Spectantium Demonstratio", but Leibniz had left virtually the same proof in an unpublished manuscript from sometime before 1683.