A q-analog of Ljunggren's binomial congruence

الأصل · EN

We prove a q-analog of a classical binomial congruence due to Ljunggren which states that a pb p ≡ ab modulo p³ for primes p≥5. This congruence subsumes and builds on earlier congruences by Babbage, Wolstenholme and Glaisher for which we recall existing q-analogs. Our congruence generalizes an earlier result of Clark.