A q-analog of Ljunggren’s binomial congruence
نویسنده
چکیده
We prove a q-analog of a classical binomial congruence due to Ljunggren which states that ap bp ! ≡ a b ! modulo p 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. Résumé. Nous démontrons un q-analogue d’une congruence binomiale classique de Ljunggren qui stipule: ap bp ! ≡ a b ! modulo p pour p premier tel que p > 5. Cette congruence s’inspire d’une précédente congruence prouvée par Babbage, Wolstenholme et Glaisher pour laquelle nous présentons les q-analogues existantes. Notre congruence généralise un précédent résultat de Clark.
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