Arithmetic properties of the Nörlund polynomial Bn(x) Original Research Article

For any prime p we establish a congruence of Kummer type for the Nörlund polynomial Bn(x), and determine the highest power of p which divides the coefficient denominators of the Nörlund polynomial. This improves the result of Carlitz (Math, Nachr. 33 (1967) 297–311), 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.