English Title

Thoughts concerning Diophantine analysis


Leonhard Euler

Enestrom Number


Original Language


Content Summary

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.

Published as

Collection article

Published Date


Original Source Citation

Commentationes arithmeticae collectae, Volume 2, pp. 576-587.

Opera Omnia Citation

Series 1, Volume 5, pp.284-302.

Record Created


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Mathematics Commons