DOAJ Open Access 2011

A $q$-analog of Ljunggren's binomial congruence

Armin Straub

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Abstrak

We prove a $q$-analog of a classical binomial congruence due to Ljunggren which states that $\binom{ap}{bp} \equiv \binom{a}{b}$ modulo $p^3$ for primes $p \geq 5$. 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.

Topik & Kata Kunci

Mathematics

Penulis (1)

Armin Straub

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Straub, A. (2011). A $q$-analog of Ljunggren's binomial congruence. https://doi.org/10.46298/dmtcs.2962

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.2962

Informasi Jurnal

Tahun Terbit: 2011
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.2962
Akses: Open Access ✓