On a class of primality criteria
Let \(\binom nk_s\) denote the generalized binomial coefficients defined by \((1+x+ \dots+ x^{s-1})^n= \sum_{k=0}^{n (s-1)} \binom nk_s x^k\), where \(s\geq 2\) is a fixed integer. Generalizing the primality criterion of \textit{H. B. Mann} and \textit{D. Shanks} [J. Comb. Theory, Ser. A 13, 131-134 (1972; Zbl 0239.10010)]\ the author proves that the number \(m\) \((m>1)\) is prime if and only if \(n\mid \binom n{m-2n}_s\) for every \(n\) with \(m/ (s+1)\leq n\leq m/2\).
scientific article; zbMATH DE number 830699