E54 -- Theorematum quorundam ad numeros primos spectantium demonstratio

(A proof of certain theorems regarding prime numbers)

(based on the abstract of David Zhao's English translation)
This paper presents the first proof of the Euler-Fermat theorem, also known as Fermat's Little Theorem, that ap-1 ≡ 1 mod p for all a relatively prime to p. Euler begins by showing that 2p-1 ≡ 1 mod p for p ≠ 2, after which he shows that 3p-1 ≡ 1 mod p for p ≠ 3. He then concludes that the formua holds for all a relatively prime to p.

According to the records, it was presented to the St. Petersburg Academy on August 2, 1736.

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