Czechoslovak Mathematical Journal, Vol. 67, No. 2, pp. 525-531, 2017
Some finite generalizations of Euler's pentagonal number theorem
Received February 10, 2016. First published March 1, 2017.
Abstract: Euler's pentagonal number theorem was a spectacular achievement at the time of its discovery, and is still considered to be a beautiful result in number theory and combinatorics. In this paper, we obtain three new finite generalizations of Euler's pentagonal number theorem.
Keywords: $q$-binomial coefficient; $q$-binomial theorem; pentagonal number theorem