English Title

Demonstration of a new method in the theory of arithmetic


Leonhard Euler

Enestrom Number


Fuss Index


Original Language


Archive Notes

According to Jacobi, a treatise with this title was read to the Berlin Academy on June 8, 1758. According to St. Petersburg Academy records, it was presented to that Academy on October 15, 1759.

Content 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 number N, prime to x, and which leaves a remainder of 1, is equal to the number of parts of N that are prime to n. In other words, the order of x modulo N is equal to the number of distinct aliquot parts of N.

Published as

Journal article

Published Date


Written Date


Original Source Citation

Novi Commentarii academiae scientiarum Petropolitanae, Volume 8, pp. 74-104.

Opera Omnia Citation

Series 1, Volume 2, pp.531-555.

Record Created


E271de.pdf (148 kB)
E271de.pdf (148 kB)