An inductive proof of Straub's q-analogue of Ljunggren's congruence

TL;DR

This paper provides an inductive proof of Straub's recently introduced q-analogue of Ljunggren's binomial congruence, enhancing understanding of q-analogues in number theory.

Contribution

The paper presents the first inductive proof of Straub's q-analogue, offering a new approach to establish this binomial congruence.

Findings

Inductive proof of Straub's q-analogue established

Enhanced understanding of q-analogues in binomial congruences

Potential applications in combinatorics and number theory

Abstract

Recently, Straub gave an interesting $q$-analogue of a binomial congruence of Ljunggren. In this note we give an inductive proof of his result.