Catalan and Motzkin numbers modulo 4 and 8

Dedicated to Professor Zhe-Xian Wan on the occasion of his 80th birthday
https://doi.org/10.1016/j.ejc.2007.06.019Get rights and content
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Abstract

In this paper, we compute the congruences of Catalan and Motzkin numbers modulo 4 and 8. In particular, we prove the conjecture proposed by Deutsch and Sagan that no Motzkin number is a multiple of 8.

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