E134 -- Theoremata circa divisores numerorum
(Theorems on divisors of numbers)
This paper contains Euler'is second proof of the Euler-Fermat theorem, which Euler presents as a consequence
of the theorem that (a+b)p = ap+bp
(mod p). This paper also includes results about possible divisors of a2n
+ b2n, and Euler uses this to show again that F5 is not prime.
to C. G. J. Jacobi, a treatise with this title was read to the Berlin Academy on March 23, 1747.
According to the records, it was presented to the St. Petersburg Academy on September 2, 1748.
Originally published in Novi Commentarii academiae scientiarum Petropolitanae 1, 1750, pp. 20-48
- Opera Omnia: Series 1, Volume 2, pp. 62 - 85
- Reprinted in Commentat. arithm. 1, 1849, pp. 50-61 [E134b]
- A handwritten French translation of this treatise can be found in the library of the observatory in
Uccle, near Brussels.
- Original publication: E134
- David Zhao of the University of Texas has an English translation of E134.
- 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 E134 include:
- Calinger R., “Leonhard Euler: The first St Petersburg years (1727-1741).” Historia Mathematica, 23 (2), pp. 121-166 (May 1996).
- Weil A., Number Theory
Return to the Euler Archive