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Keywords:
$q$-binomial coefficient; $q$-binomial theorem; pentagonal number theorem
$q$-binomial coefficient; $q$-binomial theorem; pentagonal number theorem
Summary:
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.
References:
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