Perfect powers in Catalan and Narayana numbers
Number Theory
2013-06-26 v1 Combinatorics
Abstract
When a Catalan number or a Narayana number is a (non-trivial) perfect power? For Catalan numbers, we show that the answer is "never". However, we prove that for every b, the Narayana number N(a,b) is a (non-trivial) perfect square for infinitely many values of a, and we show how to compute all of them. We also conjecture that N(a,b) is never a (non-trivial) perfect k-th power for k greater than 2 and we prove some cases of this conjecture.
Cite
@article{arxiv.1306.5929,
title = {Perfect powers in Catalan and Narayana numbers},
author = {Sara Checcoli and Michele D'Adderio},
journal= {arXiv preprint arXiv:1306.5929},
year = {2013}
}
Comments
15 pages, 2 figures