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A TRUNCATED IDENTITY OF EULER AND RELATED $q$ -CONGRUENCES

Published online by Cambridge University Press:  08 April 2020

JI-CAI LIU
Affiliation:
Department of Mathematics,Wenzhou University, Wenzhou325035, PR China email jcliu2016@gmail.com
ZHONG-YU HUANG
Affiliation:
Department of Mathematics,Wenzhou University, Wenzhou325035, PR China email 2357207357@qq.com
Corresponding

Abstract

We discuss a truncated identity of Euler and present a combinatorial proof of it. We also derive two finite identities as corollaries. As an application, we establish two related $q$ -congruences for sums of $q$ -Catalan numbers, one of which has been proved by Tauraso [‘ $q$ -Analogs of some congruences involving Catalan numbers’, Adv. Appl. Math. 48 (2012), 603–614] by a different method.

Type
Research Article
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

The first author was supported by the National Natural Science Foundation of China (grant 11801417).

References

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