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