E793 -- Considerationes circa Analysin Diophanteam
(Thoughts concerning diophantine analysis)
The first two paragraphs seem to be in praise of Diophantine analysis. Then we turn to familiar ground:
- Find three numbers, v, x, and y that make the following expressions squares:
vx + v + x, vy + v + y, xy + x + y.
- Find four numbers that make the following squares: AB - 1, AC - 1, AD - 1, BC - 1, BD - 1,
CD - 1. Easy solution: 1, 2, 5, 1.
- Given a number n, find four numbers that make squares out of AB + n, AC + n, etc.
Originally published in Commentationes arithmeticae 2, 1849, pp. 576-587
Opera Omnia: Series 1, Volume 5, pp. 284 - 302
- Reprinted in Opera postuma 1, 1862, pp. 128-139 [E793a]
- Original publication: E793
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