Czechoslovak Mathematical Journal, online first, 7 pp.

Some finite generalizations of Euler's pentagonal number theorem

Ji-Cai Liu

Received February 10, 2016.   First published March 1, 2017.

Ji-Cai Liu, College of Mathematics and Information Science, Wenzhou University, 276 Xueyuan Middle Road, Wenzhou, 325027, Zhejiang, P. R. China, e-mail:

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

Classification (MSC 2010): 05A17, 11B65

DOI: 10.21136/CMJ.2017.0063-16

Full text available as PDF.

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