E556 -- De criteriis aequationis fxx + gyy = hxx, utrum ea resolutionem admittat necne?
(On the criteria of whether equation fxx + gyy = hxx admits a resolution or not)
Summary:
Euler's motivating example is that xx + yy + 2zz has solutions but that
xx + yy = 3zz has no solutions. The question is, what values of those letters
f, g and h give equations that have solutions? He shows, given an f, a g,
and three values of h for which there are solutions, how to construct a fourth value of h, and calls it
(section 12) a most elegant theorem.
According to the records, it was presented to the St. Petersburg Academy on December 7, 1772.
Publication:
-
Originally published in Opuscula Analytica 1, 1862, pp. 211-241
-
Opera Omnia: Series 1, Volume 4, pp. 1 - 24
- Reprinted in Commentat. arithm. 2, 1849, pp. 556-569 [E556a]
Documents Available:
- Original Publication: E556
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