On two congruences involving Apéry and Franel numbers

Abstract

In this paper, we generalise a congruence which proved by V. J.-W. Guo and J. Zeng \cite{gz-jnt-2012} involving Apéry 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}.

11pages

Cited by in corpus (2)

• Proof of some congruence conjectures of Z.-H. Sun involving Apéry-like numbers
• On two congruence conjectures of Z.-W. Sun involving Franel numbers