E98 -- Theorematum quorundam arithmeticorum demonstrationes
(The proofs of some arithmetic theorems)
Summary:
Euler proves that the sum of two 4th powers can't be a 4th power, and that the difference of two distinct non-zero 4th powers can't be a 4th power and other such forms.
According to the records, it was presented to the St. Petersburg Academy on June 23, and August 16
(Additions), 1738.
Publication:
-
Originally published in Commentarii academiae scientiarum Petropolitanae 10, 1747, pp. 125 - 146
-
Opera Omnia: Series 1, Volume 2, pp. 38 - 58
- Reprinted in Commentat. arithm. 1, 1849, pp. 24 - 34 [98a]
- A translation of selections of E262 is published in D. J. Struik's
A Source Book in Mathematics, 1200-1800 (1969, Harvard University Press), pp. 36 - 40.
- According to Eneström, a handwritten French translation of this treatise can be found in
the library of the observatory in Uccle, near Brussels.
Documents Available:
- Original publication: E098 (in the Commentarii)
- German translation (Artur Diener and Alexander Aycock): E098
- Portuguese translation (Marcelo Cardoso): E098
- 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 E98 include:
- Calinger R., “Leonhard Euler: The first St Petersburg years (1727-1741).” Historia Mathematica, 23 (2), pp. 121-166 (May 1996).
- Dickson
- Lemmermeyer F., “A note on Pepin's counter examples to the Hasse principle for curves of genus 1.” Abhandlungen Aus Dem Mathematischen Seminar der Universitat Hamburg, 69, pp. 335-345 (1999).
- Weil A., Number Theory
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