On two congruences involving Ap\'ery and Franel numbers

Abstract

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

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