The solution of a problem about searching for three numbers, of which the sum and not only their product but the sum of their products two apiece, are square numbers
According to Jacobi, a treatise with almost the same title appears to have been read to the Berlin Academy on February 27, 1755. According to St. Petersburg Academy records, it was presented to that Academy on March 8, 1756.
Euler wants all of the numbers n(x+y+z), nn(xy+xz+yz) and n3xyz to be squares, where x, y, and z are rational.
Original Source Citation
Novi Commentarii academiae scientiarum Petropolitanae, Volume 8, pp. 64-73.
Opera Omnia Citation
Series 1, Volume 2, pp.519-530.