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

中文翻译：

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关于包含 Apéry 和 Franel 数的两个同余

在本文中，我们概括了由 VJ-W 证明的同余。Guo 和 J. Zeng \cite{gz-jnt-2012} 涉及 Apery 数，我们获得了涉及 Franel 数的同余，这证实了 Z.-W 的同余猜想。Sun \cite[猜想 57(ii)]{sun-njdx-2019}。