E271 -- Theoremata arithmetica nova methodo demonstrata

(Demonstration of a new method in the Theory of Arithmetic)


Summary:

Euler presents a third proof of the Fermat theorem, the one that lets us call it the Euler-Fermat theorem. This seems to be the proof that Euler likes best. He also proves that the smallest power xn that, when divided by a numer N, prime to x, and that leaves a remainder of 1, is equal to the number of parts of N that are prime to n, that is to say, the number of distinct aliquot parts of N.

According to C. G. J. Jacobi, a treatise with this title was read to the Berlin Academy on June 8, 1758.

According to the records, it was presented to the St. Petersburg Academy on October 15, 1759.

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