We establish a q-analogue of Sun-Zhao's congruence on harmonic sums. Based on this q-congruence and a q-series identity, we prove a congruence conjecture on sums of central q-binomial coefficients, which was recently proposed by Guo. We also deduce a q-analogue of a congruence due to Apagodu and Zeilberger from Guo's q-congruence.

In 1997, van Hamme conjectured 13 Ramanujan-type supercongruences labeled (A.2)-(M.2). Using some combinatorial identities discovered by Sigma, we extend (A.2) and (H.2) to supercongruences modulo p 4 for primes p ≡ 3 (mod 4), which appear to be new.

On a congruence involving q-Catalan numbers

No abstract

No abstract