Thoughts concerning Diophantine analysis
The first two paragraphs seem to be in praise of Diophantine analysis. Then we turn to familiar ground: first, find three numbers, v, x, y that make squares out of the expressions vx+v+x, vy+v+y, and xy+x+y. Next, find four numbers A, B, C, D that make the following squares: AB–1, AC–1, AD–1, BC–1, BD–1, and CD–1. (An easy solution is 1, 2, 5, 1.) Given a number n, find four numbers that make squares out of AB+n, AC+n, etc.
Original Source Citation
Commentationes arithmeticae collectae, Volume 2, pp. 576-587.
Opera Omnia Citation
Series 1, Volume 5, pp.284-302.