Denote by the Stirling numbers of the second kind (, positive integers), which are defined by the following recurrence formula
In this paper the author proves the following two congruences concerning the Stirling numbers and the Bernoulli numbers :
where is a prime and an integer, .
The proof uses the congruence , , from the preceding paper of the author [ibid. 30, 1-9 (1990)] and some equalities among the numbers . Using again the congruence and polynomials the author gives the interesting equality