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

Authors

Leonhard Euler

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

Included in

Mathematics Commons

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