%0 Generic %1 citeulike:3036281 %A Euler, Leonhard %D 2005 %K Vor1800 available-in-tex-format mathematics number-theory pre1800 %T Demonstration of a theorem about the order observed in the sums of divisors %U http://arxiv.org/abs/math/0507201 %X Euler proves that the infinite product s=(1-x)(1-x^2)(1-x^3)... expands into the power series s=1-x-x^2+x^5+x^7-..., in which the signs alternate in two's and the exponents are the pentagonal numbers. Euler uses this to prove his pentagonal number theorem, a recurrence relation for the sum of divisors of a positive integer.

@misc{citeulike:3036281, abstract = {Euler proves that the infinite product s=(1-x)(1-x^2)(1-x^3)... expands into the power series s=1-x-x^2+x^5+x^7-..., in which the signs alternate in two's and the exponents are the pentagonal numbers. Euler uses this to prove his pentagonal number theorem, a recurrence relation for the sum of divisors of a positive integer.}, added-at = {2009-08-02T17:14:35.000+0200}, archiveprefix = {arXiv}, author = {Euler, Leonhard}, biburl = {https://www.bibsonomy.org/bibtex/2dac222a67f62c9ba6426422f4c378996/rwst}, citeulike-article-id = {3036281}, citeulike-linkout-0 = {http://arxiv.org/abs/math/0507201}, citeulike-linkout-1 = {http://arxiv.org/pdf/math/0507201}, description = {my bookmarks from citeulike}, eprint = {math/0507201}, interhash = {39e2a6d330e95afec95338563bc66300}, intrahash = {dac222a67f62c9ba6426422f4c378996}, keywords = {Vor1800 available-in-tex-format mathematics number-theory pre1800}, month = Jul, posted-at = {2008-07-23 08:48:03}, priority = {2}, timestamp = {2009-08-06T10:24:00.000+0200}, title = {Demonstration of a theorem about the order observed in the sums of divisors}, url = {http://arxiv.org/abs/math/0507201}, year = 2005 }