International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 4, Pages 677-684
doi:10.1155/S0161171279000508
Arithmatical consequences of two identities of B. Gordon
Department of Mathematical Sciences, Northern Illinois University, Dekalb 60115, Illinois, USA
Received 28 May 1979
Copyright © 1979 John A. Ewell. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
From two partition identities of Basil Gordon the author derives two recursive formulas for the sum-of-divisors function. A third application yields an alternate proof of Rmanujan's theorem on the divisibility of certain values of the partition function by the modulus 5.