English Title

A theorem of arithmetic and its proof

Authors

Leonhard Euler

Enestrom Number

794

Original Language

Latin

Content Summary

In this paper, Euler proves that for m unequal positive integers a, b, c, d, ..., the sum of fractions an/[(ab)(ac)(ad)...] + bn/[(ba)(bc)(bd)...] + cn/[(ca)(cb)(cd)...] + dn/[(da)(db)(dc)...] + ... is equal to 0 for nm–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)....

Published as

Collection article

Published Date

1849

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

E794en.pdf (92 kB)
E794en.pdf (92 kB)

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