The odd Catalan numbers modulo 2^k

Details The odd Catalan numbers modulo 2^k The odd Catalan numbers modulo 2^k

2010-12-08

arxiv.org/abs/1012.1756v2

Mathematics

Number Theory

6 pages

Scientific paper

We study the properties of the odd Catalan numbers, C_n, modulo 2^k for k >=
2. We show that there exist only k - 1 different congruences of the odd Catalan
numbers modulo 2^k. Moreover, these congruences can be obtained by C_{2^m - 1}
(mod 2^k) for m = 1, 2, ..., k - 1.

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