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.)

Topic

Number Theory

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