A Simple Proof of Schmidt's Conjecture

Abstract

For any integer $r\ge 1$, the sequence of numbers $\{c_k^{(r)}{\}}_{k\ge 0}$ is defined implicitly by [\sum_k\binom{n}{k}^r\binom{n+k}{k}^r = \sum_k\binom{n}{k}\binom{n+k}{k}c^{(r)}_k,\quad n=0,1,2,...] Asmus Schmidt conjectured that all $c_k^{(r)}$ are integers. We give a new proof of this fact.

4 pages

References in corpus (1)

• Proof of some conjectures of Z.-W. Sun on congruences for Apery polynomials