Proof of Two Conjectural q-Supercongruences Related to Van Hamme's (G.2) Supercongruence
Liton Karmakar, Arijit Jana
Abstract
In this paper, we prove two conjectures concerning parametric q- supercongruences related to Van Hamme's (G.2) supercongruence. First, we confirm Tang s conjecture [Conjecture 4.1]Tang G2 by establishing the corresponding congruences modulo [m]Φm(q)2. Second, we prove a conjecture of Wang and Xu [Conjecture 2]WangXu24, extending their q-supercongruence modulo Φm(q)5 to modulo [m]Φm(q)4 when m14.
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