English Title

A proof of certain theorems regarding prime numbers

Authors

Leonhard Euler

Enestrom Number

54

Fuss Index

24

Original Language

Latin

Published as

Journal article

Published Date

1741

Written Date

1736

Content Summary

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 any prime other than 2, after which he shows that 3p-1 = 1 (mod p) for any prime other than 3. He then concludes via mathematical induction that the formula holds for all a relatively prime to p. (Based on David Zhao's translation abstract.)

Original Source Citation

Commentarii academiae scientiarum Petropolitanae, Volume 8, pp. 141-146.

Opera Omnia Citation

Series 1, Volume 2, pp.33-37.

Record Created

2018-09-25

Included in

Mathematics Commons

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