MULTIPLE HARMONIC SUMS AND WOLSTENHOLME'S THEOREM

作者：Rosen Julian^*

来源：International Journal of Number Theory, 2013, 9(8): 2033-2052.

DOI：10.1142/S1793042113500735

• Multiple harmonic sums
• binomial coefficients

We give a family of congruences for the binomial coefficient ((kp-1)(p-1)), with k an integer and p a prime. Our congruences involve multiple harmonic sums, and hold modulo arbitrary large powers of p. The general congruence in our family, which depends on a parameter n, involves n "elementary symmetric" multiple harmonic sums, and holds modulo p(2n+3). These congruences are actually part of a much larger collection of congruences for ((kp-1)(p-1)) in terms of the elementary symmetric multiple harmonic sums. Congruences in our family have been optimized, in that they involve the fewest multiple harmonic sums among those congruences holding modulo the same power of p. The coefficients in our congruences are given by polynomials in k.

• 出版日期2013-12