Theorema arithmeticum eiusque demonstratio

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/[(a–b)(a–c)(a–d)...] + bⁿ/[(b–a)(b–c)(b–d)...] + cⁿ/[(c–a)(c–b)(c–d)...] + dⁿ/[(d–a)(d–b)(d–c)...] + ... 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 (z–a)(z–b)(z–c)....

Topics

Theory of Equations

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