The odd Catalan numbers modulo 2k
Abstract
We study the properties of the odd Catalan numbers, Cn, modulo 2k for k >= 2. We show that there exist only k - 1 different congruences of the odd Catalan numbers modulo 2k. Moreover, these congruences can be obtained by C2m - 1 (mod 2k) for m = 1, 2, ..., k - 1.
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