English

On two congruences involving Ap\'ery and Franel numbers

Number Theory 2021-11-18 v1 Combinatorics

Abstract

In this paper, we generalise a congruence which proved by V. J.-W. Guo and J. Zeng \cite{gz-jnt-2012} involving Ap\'{e}ry numbers, and we obtain a congruence involving Franel numbers which confirms a congruence conjecture of Z.-W. Sun \cite[Conjecture 57(ii)]{sun-njdx-2019}.

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Cite

@article{arxiv.2003.10206,
  title  = {On two congruences involving Ap\'ery and Franel numbers},
  author = {Guo-Shuai Mao},
  journal= {arXiv preprint arXiv:2003.10206},
  year   = {2021}
}

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11pages