In this paper, Euler proves that for m unequal positive integers a,b,c,d,...,
the sum of the fractions: a^n/(a-b)(a-c)(a-d)... + b^n/(b-a)(b-c)(b-d)... +
c^n/(c-a)(c-b)(c-d)... + d^n/(d-a)(d-b)(d-c)... + ... is equal to 0 for n
less than or equal to m-2, and he gives a general formula for the sum of these
fractions for n equal m-1, m and greater than 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)... The end of the Latin original
is missing.
%0 Generic
%1 citeulike:3036297
%A Euler, Leonhard
%D 2005
%K Vor1850 available-in-tex-format mathematics number-theory pre1850
%T A theorem of arithmetic and its proof
%U http://arxiv.org/abs/math/0502425
%X In this paper, Euler proves that for m unequal positive integers a,b,c,d,...,
the sum of the fractions: a^n/(a-b)(a-c)(a-d)... + b^n/(b-a)(b-c)(b-d)... +
c^n/(c-a)(c-b)(c-d)... + d^n/(d-a)(d-b)(d-c)... + ... is equal to 0 for n
less than or equal to m-2, and he gives a general formula for the sum of these
fractions for n equal m-1, m and greater than 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)... The end of the Latin original
is missing.
@misc{citeulike:3036297,
abstract = {In this paper, Euler proves that for m unequal positive integers a,b,c,d,...,
the sum of the fractions: a^n/{(a-b)(a-c)(a-d)...} + b^n/{(b-a)(b-c)(b-d)...} +
c^n/{(c-a)(c-b)(c-d)...} + d^n/{(d-a)(d-b)(d-c)...} + ... is equal to 0 for n
less than or equal to m-2, and he gives a general formula for the sum of these
fractions for n equal m-1, m and greater than 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)... The end of the Latin original
is missing.},
added-at = {2009-08-02T17:14:35.000+0200},
archiveprefix = {arXiv},
author = {Euler, Leonhard},
biburl = {https://www.bibsonomy.org/bibtex/2ea9a46b8a4c9e42957ab7089ace26546/rwst},
citeulike-article-id = {3036297},
citeulike-linkout-0 = {http://arxiv.org/abs/math/0502425},
citeulike-linkout-1 = {http://arxiv.org/pdf/math/0502425},
description = {my bookmarks from citeulike},
eprint = {math/0502425},
interhash = {2ac537d1ef22802356b17123fe73e4de},
intrahash = {ea9a46b8a4c9e42957ab7089ace26546},
keywords = {Vor1850 available-in-tex-format mathematics number-theory pre1850},
month = Feb,
posted-at = {2008-07-23 08:54:23},
priority = {2},
timestamp = {2009-08-06T10:27:50.000+0200},
title = {A theorem of arithmetic and its proof},
url = {http://arxiv.org/abs/math/0502425},
year = 2005
}