 
Summary: This is a condensed version of the full paper, containing the complete Introduction, all
statements of Lemma, Theorems, and Corollaries, some of the Remarks, and the Bibliog
raphy. The full version can be obtained from the author.
Arithmetic properties of the Nšorlund polynomial B (x)
n
Arnold Adelberg
Dedicated to H. W. Gould on the occasion of his 70th birthday.
Abstract
For any prime p we establish a congruence of Kummer type for the Nšorlund polynomial
B (x)
n , and determine the highest power of p which divides the coefficient denominators of
the Nšorlund polynomial. This improves the result of [4] where only an upper bound was
proven. We deduce a simple formula for the least common denominator of the coefficients.
Applications are made for the Stirling polynomials.
Keywords Nšorlund polynomials, Bernoulli numbers and polynomials, Stirling polynomi
als, Kummer congruences.
1. Introduction
We are pleased to contribute to this volume dedicated to H. W. Gould, whose collection
of binomial identities [6] led us into the field of Bernoulli and related polynomials [2].
The Nšorlund polynomials B (x)
