Recherches sur le probleme de trois nombres carres tels que la somme de deux quelconques moins le troisieme fasse un nombre carre

English Title

Research into the problem of three square numbers such that the sum of any two less the third one provides a square number

Authors

Leonhard Euler

Enestrom Number

796

Original Language

Latin

Content Summary

In the first part, Euler presents several different methods of finding values of x, y, and z that make the following three expressions all squares: yy+zz–xx, xx+zz–yy, xx+yy–zz. In the second part, entitled "Solution to a rather curious known problem: to find four positive numbers, unequal among themselves, such that the sum of any two is always a square," Euler presents several solutions, by familiar means. The third part is entitled "Supplement to the problem of four given numbers of which the sum of two always makes a square number."

Published as

Collection article

Published Date

1849

Written Date

1781

Original Source Citation

Commentationes arithmeticae collectae, Volume 2, pp. 603-616.

Opera Omnia Citation

Series 1, Volume 5, pp.303-329.

Record Created

2018-09-25