#### 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

#### Enestrom Number

796

#### Original Language

Latin

#### Published as

Collection article

#### Published Date

1849

#### Written Date

1781

#### 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."

#### 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