Polynomial reduction and supercongruences

摘要

Based on a reduction process, we rewrite a hypergeometric term as the sum of the difference of a hypergeometric term and a reduced hypergeometric term (the reduced part, in short). We show that when the initial hypergeometric term has a certain kind of symmetry, the reduced part contains only odd or even powers. As applications, we derived two infinite families of supercongruences. (C) 2019 Elsevier Ltd. All rights reserved.