English Title

Thoughts concerning Diophantine analysis

Authors

Leonhard Euler

Enestrom Number

793

Original Language

Latin

Published as

Collection article

Published Date

1849

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.

Original Source Citation

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

Opera Omnia Citation

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

Record Created

2018-09-25

Included in

Mathematics Commons

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