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World Scientific Publishing, International Journal of Number Theory, 05(16), p. 981-1003, 2019

DOI: 10.1142/s1793042120500505

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Congruences for Apéry numbers βn =∑k=0nn k2n+k k

Journal article published in 2019 by Hui-Qin Cao, Yuri Matiyasevich, Zhi-Wei Sun
This paper was not found in any repository, but could be made available legally by the author.
This paper was not found in any repository, but could be made available legally by the author.

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Abstract

In this paper, we establish some congruences involving the Apéry numbers [Formula: see text]. For example, we show that [Formula: see text] for any positive integer [Formula: see text], and [Formula: see text] for any prime [Formula: see text], where [Formula: see text] is the [Formula: see text]th Bernoulli number. We also present certain relations between congruence properties of the two kinds of Aṕery numbers, [Formula: see text] and [Formula: see text].