Binary partitions revisited
The binary partition function \(b_k(n)\) counts the number of representations of \(n\) as a sum of not necessarily distinct powers of 2 strictly less than \(2^k\). The authors prove that for \(1 \leq r \leq k-2\), we have \(b_k(2^{r+2}n)-b_{k-2}(2^rn) \equiv 0 \pmod{2^{\lfloor 3r/2\rfloor+2}}. \) For \(k \geq 3\) and \(t \geq 1\), we have \(b_k(2^{k+t}n)-b_k(2^{k+t-2}n) \equiv 0 \pmod{2^{\lfloor 3k/2\rfloor+t+2}}\).
scientific article; zbMATH DE number 1760665