On a Combinatorial Problem of Asmus Schmidt

For any integer r 2, define a sequence of numbers {c (r) k }k=0,1,..., independent of the parameter n, by n k=0 n k r n + k k r = n k=0 n k n + k k c (r) k , n = 0, 1, 2, . . . . We prove that all the numbers c (r) k are integers. 1 Stating the problem The following curious problem was stated by A. L. Schmidt in [5] in 1992.

• Type: Journal
• Year: 2004
• Where: COMBINATORICS
• Authors: W. Zudilin
• Keywords: COMBINATORICS 2004, Integer, Parameter, Schmidt