SUPERCONGRUENCES CONCERNING BISNOMIAL COEFFICIENTS

We establish two supercongruences for bisnomial coefficients. We give a supercongruence similar to Jacobsthal’s binomial congruence, and as a consequence, we confirm the following conjecture for trinomial coefficients: nprkpr2≡npr−1kpr−12(mod⁡p2r), where n,k be nonnegative integers and r≥1 is an integer with p>3 is an odd prime number, which were posed by G.-S. Mao [On some congruences involving trinomial coefficients. Rocky Mountain J. Math. 50(5) (2020), 1759–1771]. We also generalize the Ljunggren congruence for binomial coefficients to bisnomial coefficients.