E542 -- De mirabilinus proprietatibus numerorum pentagonalium
(On the remarkable properties of the pentagonal numbers)
(based on Jordan Bell's abstract)
Euler considers properties of the pentagonal numbers, those numbers of the form (3n2 ± n)/2. He
starts with the series in E541 and notices that some of its exponents are
pentagonal numbers. He then tries to substitute the roots of the infinite product into the series.
According to the records, it was presented to the St. Petersburg Academy on September 4, 1775.
Originally published in Acta Academiae Scientarum Imperialis Petropolitinae 1780, 1783, pp. 56-75
Opera Omnia: Series 1, Volume 3, pp. 480 - 496
- Reprinted in Commentat. arithm. 2, 1849, pp. 105-115 [E542a]
- A handwritten French translation of this treatise can be found in the library of the observatory in
Uccle, near Brussels.
- Original Publication: E542
- English translation (Jordan Bell): E542
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