A CONGRUENCE FOR THE FERMAT QUOTIENT MODULO p3

摘要

For a prime p > 3 and the Fermat quotient qp(2) = (2p1 1)/p, Z.H. Sun proved that Xp1 k=1 2k k + 2qp(2) 7 12p2Bp3 (mod p3), where Bn is the n-th Bernoulli number. In this note, we give an elementary proof of this congruence.