E792 -- Tractatus de numerorum doctrina capita sedecim, quae supersunt
(English Translation of Title)
Summary:
This is Euler’s beginning of a book on number theory, in 17 chapters. Quadratic residues start in section 343,
cubic residues in Chapter 11, section 370. Starting in paragraph 400, Feuter notes that some of Euler’s proofs are incomplete.
Publication:
-
Originally published in Commentationes arithmeticae 2, 1849, pp. 503-575
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Opera Omnia: Series 1, Volume 5, pp. 182 - 283
- Reprinted in Opera postuma 1, 1862, pp. 3-75 [E792a]
Documents Available:
- Original publication:
- chapter 1: De compositione numerorum
- chapter 2: De divisoribus numerorum
- chapter 3: De summa divisorum cujusque numeri
- chapter 4: De numeris inter se primis et compositis
- chapter 5: De residuis, ex divisione natis
- chapter 6: De residuis, ex divisione terminorum progressionis arithmeticae ortis
- chapter 7: De residuis, ex divisione terminorum progressionis geometricae ortis
- chapter 8: De potestatibus nomerorum, quae per numeros primos divisae, unitatem relinquunt
- chapter 9: De divisoribus numerorum formae an ±
bn
- chapter 10: De residuis, ex divisione quadratorum per numeros primos ortis
- chapter 11: De residuis, ex divisione cuborum per numeros primos natis
- chapter 12: De residuis, ex divisione biquadratorum per numeros primos ortis
- chapter 13: De residuis, ex divisione surdesolidorum per numeros primos ortis
- chapter 14: De residuis, ex divisione quadratorum per numeros compositos ortis
- chapter 15: De divisoribus numeroum formae xx + yy
- chapter 16: De divisoribus numerorum formae xx + 2yy
- An English draft translation of this work has been completed by John Fossa: E792
- Other works that cite this paper include:
- Dickson
- Andre Weil, Number Theory
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