#### English Title

On finding three or more numbers, the sum of which is a square, while the sum of the squares is a fourth power

#### Enestrom Number

763

#### Fuss Index

44

#### Original Language

Latin

#### Published as

Journal article

#### Published Date

1824

#### Written Date

1780

#### Content Summary

Euler attributes this problem to Fermat and says he heard it from Lagrange: to find three numbers, *x*, *y*, and *z* such that *x*+*y*+*z* is a square and *xx*+*yy*+*zz* is a fourth power. He starts with a two-variable problem, asking that *x*+*y* be square and *xx*+*yy* a fourth power. He finds a pair of numbers in the trillions. Then he finds a three-variable solution *x*=49, *y*=64, *z*=8 and goes on to four variables (*x*=193, *y*=104, *z*=48, *v*=16) and even five variables.

#### Original Source Citation

Mémoires de l'académie des sciences de St.-Petersbourg, Volume 9, pp. 3-13.

#### Opera Omnia Citation

Series 1, Volume 5, pp.61-70.

#### Record Created

2018-09-25