Polynomial Reduction and Super Congruences

Qing-Hu Hou, Yan-Ping Mu, Doron Zeilberger

Published 2019-07-17Version 1

Based on a reduction processing, 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 super-congruences.