%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 }