Guoping Gu, Xiaoxia Wang: A family of $q$-analogues for a congruence by Sun, 159-167

Abstract:

Recently, Guo conjectured two $q$-analogues for a congruence discovered by Sun, which were subsequently verified by Liu and Qi. In this paper, we provide a family of $q$-analogues for the same Sun's congruence by utilizing Carlitz's identity and a $q$-analogue of Morley's congruence.

Key Words: Combinatorial congruence, $q$-congruence, cyclotomic polynomial, $q$-supercongruence, Carlitz's formula.

2020 Mathematics Subject Classification: Primary 33C20; Secondary 05A10, 33D15.

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