#### Title

#### English Title

Miscellaneous analyses

#### 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