# Polynomial Reduction and Super Congruences

## TL;DR

This paper introduces a polynomial reduction method for hypergeometric terms, revealing symmetry properties that lead to new super-congruences, advancing understanding in hypergeometric and number theory.

## Contribution

It presents a novel polynomial reduction technique for hypergeometric terms and derives new infinite families of super-congruences based on symmetry properties.

## Key findings

- Reduced hypergeometric terms contain only odd or even powers under symmetry
- Derived two infinite families of super-congruences
- Enhanced understanding of hypergeometric term reductions

## Abstract

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.