English Title

Miscellaneous analyses

Authors

Leonhard Euler

Enestrom Number

560

Fuss Index

40

Original Language

Latin

Published as

Collection article

Published Date

1783

Written Date

1773

Content Summary

This starts with a proof of what Euler calls Waring's theorem, now known as Wilson's theorem, that (n-1)! is congruent to 1 modulo n if n is prime. The next problem is to find four numbers whose pairwise products, increased by 1, give squares. He also cites a problem posed by Leibniz: find two numbers, p and q, so that their sum is a square and the sum of their squares is a fourth power.

Original Source Citation

Opuscula analytica, Volume 1, pp. 329-344.

Opera Omnia Citation

Series 1, Volume 4, pp.91-104.

Record Created

2018-09-25

Included in

Mathematics Commons

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