E164 -- Theoremata circa divisores numerorum in hac forma paa ± qbb contentorum
(Theorems about the divisors of numbers contained in the form paa ± qbb )
Summary:
A first page footnote by Rudio warns us that Euler says that most of these theorems are known to him only by "induction;" their proofs appear in other places. This seems to be a forgotten little article, hardly any proofs, but it contains a lot of conjectures that kept him going for the next
several years.
According to the records, it was presented to the St. Petersburg Academy on
September 23, 1748.
Publication:
-
Originally published in Commentarii academiae scientiarum Petropolitanae 14, 1751, pp. 151-181
-
Opera Omnia: Series 1, Volume 2, pp. 194 - 222
- According to C. G. J. Jacobi, the manuscript can be found in the archive of the Berlin Academy and appears to have been read there in 1747.
- Reprinted in Commentat. arithm. 1, 1849, pp. 35-39 [E164a]
Documents Available:
- Original publication: E164
(in the Commentarii)
- English Translation (Jordan Bell): E164
- E164 is discussed in Ed Sandifer's How Euler Did It December
2005 column published online by the MAA.
- The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E164 include:
- Edwards HM., “Euler and quadratic reciprocity.” Mathematics Magazine, 56 (5), pp. 285-291 (1983).
Return to the Euler Archive