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Some supercongruences occurring in truncated hypergeometric series. (English) Zbl 1336.33018

The authors prove supercongruences involving hypergeometric functions and \(p\)-adic gamma functions. These imply, among others a conjecture by J. Kibelbek et al. [J. Number Theory 164, 166–178 (2016; Zbl 1334.33020)], and a strenghened version of a conjecture by L. van Hamme [Lect. Notes Pure Appl. Math. 192, 223–236 (1997; Zbl 0895.11051)].

MSC:

33C20 Generalized hypergeometric series, \({}_pF_q\)
11D88 \(p\)-adic and power series fields
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