New q-supercongruences arising from a summation of basic hypergeometric series

Abstract

With the help of a summation of basic hypergeometric series, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials, we prove some new q-supercongruences on sums of q-shifted factorials. Especially, we give a q-analogue of a formula due to Liu [14].

Keywords

• q-supercongruence
• basic hypergeometric series
• creative microscoping method
• chinese remainder theorem for coprime polynomials