E586 -- Considerationes super theoremate Fermatiano de resolutione numerorum in numeros polygonales
(Considerations about a theorem of Fermat on the resolution of numbers into polygonal numbers)
Summary:
Euler considers Fermat’s "theorem," that any number is the sum of n or fewer n-gonal numbers. He works with the generating function approach.
According to the records, it was presented to the St.
Petersburg Academy on December 12, 1774.
Publication:
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Originally published in Opuscula Analytica 2, 1785, pp. 3-15.
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Opera Omnia: Series 1, Volume 4, pp. 125 - 135
- Reprinted in Commentat. arithm. 2, 1849, pp. 92-98 [E586a]
Documents Available:
- Original Publication: E586
- 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 E586 include:
- Barbeau EJ., “Euler subdues a very obstreperous series.” American Mathematical Monthly, 86 (5), pp. 356-372 (1979).
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