SCI Библиотека

Let p be an odd prime number. In this paper, among other results, we establish some congruences involving inverse of binomial coefficients. These congruences are mainly determined modulo p, p2, p3 and p4 in the p-integers ring in terms of Fermat quotients, harmonic numbers and Bernoulli numbers in a simple way. Furthermore, we extend an interesting theorem of E. Lehmer to the class of inverse binomial coefficients.