English Title

A theorem of arithmetic and its proof

Authors

Leonhard Euler

Enestrom Number

794

Original Language

Latin

Published as

Collection article

Published Date

1849

Content Summary

In this paper, Euler proves that for m unequal positive integers a, b, c, d, ..., the sum of the fractions: an/[(ab)(ac)(ad)...] + bn/[(ba)(bc)(bd)...] + cn/[(ca)(cb)(cd)...] + dn/[(da)(db)(dc)...} + ... is equal to 0 for n≤m–2, and he gives a general formula for the sum of these fractions for n=1, n=m and n>m. He shows a direct relationship between the values of the sum of these fractions for higher n and the coefficients of the polynomial (za)(zb)(zc)....

Original Source Citation

Commentationes arithmeticae collectae, Volume 2, pp. 588-592.

Opera Omnia Citation

Series 1, Volume 6, pp.486-493.

Record Created

2018-09-25

Included in

Mathematics Commons

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