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## Congruence properties of binary partition functions

### Abstract

Let A be a finite subset of the natural numbers containing 0, and let f(n) denote the number of ways to write n in the form $\sum e_j2^j$, where $\e_j \in A$. We show that there exists a computable T = T(A) so that the sequence (f(n) mod 2) is periodic with period T. Variations and generalizations of this problem are also discussed

Topics: Mathematics - Number Theory, Mathematics - Combinatorics, Primary:11A63, 11B50, 11P81
Year: 2011
OAI identifier: oai:arXiv.org:1102.5355