A solution of several Diophantine problems
Euler is searching for squares, with the standing assumption is that two pairs of squares xx, yy and tt, uu are given. In the first problem, he wants (xx+yy)(ttxx+uuyy) and (xx+yy)(uuxx+ttyy) to be squares. In the second problem, he wants (ttxx + uuyy)(uuxx+ttyy) to be a square. Lastly, he wants ttxx+uuyy and ttyy+uuxx to be squares.
Original Source Citation
Novi Commentarii academiae scientiarum Petropolitanae, Volume 20, pp. 48-58.
Opera Omnia Citation
Series 1, Volume 3, pp.405-417.