Proof of Sun's conjectural supercongruence involving Catalan numbers

Ji-Cai Liu; Ji-Cai Liu

doi:10.3934/era.2020054

Electronic Research Archive

2020, Volume 28, Issue 2: 1023-1030. doi: 10.3934/era.2020054

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Proof of Sun's conjectural supercongruence involving Catalan numbers

Ji-Cai Liu

Department of Mathematics, Wenzhou University, Wenzhou 325035, China

Received: 01 January 2020 Revised: 01 April 2020
Primary: 11A07, 11B65; Secondary: 05A19, 33C20

We confirm a conjectural supercongruence involving Catalan numbers, which is one of the 100 selected open conjectures on congruences of Sun. The proof makes use of hypergeometric series identities and symbolic summation method.
- Supercongruences,
- Catalan numbers,
- Fermat quotients
Citation: Ji-Cai Liu. Proof of Sun's conjectural supercongruence involving Catalan numbers[J]. Electronic Research Archive, 2020, 28(2): 1023-1030. doi: 10.3934/era.2020054

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Abstract

We confirm a conjectural supercongruence involving Catalan numbers, which is one of the 100 selected open conjectures on congruences of Sun. The proof makes use of hypergeometric series identities and symbolic summation method.

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