Demonstratio theorematis circa ordinem in summis divisorum observatum

English Title

A demonstration of a theorem on the order observed in the sums of divisors

Authors

Leonhard Euler

Enestrom Number

244

Fuss Index

18

Original Language

Latin

Content Summary

Euler proves that the infinite product s = (1–x)(1–x²)(1–x³)... expands into the power series s = 1 – x – x² + x⁵ + x⁷ – ..., in which the signs alternate in twos and the exponents are the pentagonal numbers. Euler uses this to prove his pentagonal number theorem, a recurrence relation for the sum of divisors of a positive integer. (From Jordan Bell's translation summary.)

Published as

Journal article

Published Date

1760

Written Date

1760

Original Source Citation

Novi Commentarii academiae scientiarum Petropolitanae, Volume 5, pp. 75-83.

Opera Omnia Citation

Series 1, Volume 2, pp.390-398.

Record Created

2018-09-25