For every integer k, a k-representation of $2^{k-1}$ is a string $\n=(n_1, \ldots,n_k)$ of nonnegative integers such that $\sum_{j=1}^k 2^{n_j} = 2^{k-1}$, and W(1,k) is their number. We present an efficient recursive formula for W(1,k); this formula allows also to prove the congruence $W(1,k) = 4+(-1)^k\pmod{8}$ for $k\geq 3$.
Representation of a 2-power as sum of k 2-powers: a recursive formula / A. Giorgilli, G. Molteni. - In: JOURNAL OF NUMBER THEORY. - ISSN 0022-314X. - 133:4(2013 Apr), pp. 1251-1261.
Representation of a 2-power as sum of k 2-powers: a recursive formula
A. Giorgilli;G. Molteni
2013
Abstract
For every integer k, a k-representation of $2^{k-1}$ is a string $\n=(n_1, \ldots,n_k)$ of nonnegative integers such that $\sum_{j=1}^k 2^{n_j} = 2^{k-1}$, and W(1,k) is their number. We present an efficient recursive formula for W(1,k); this formula allows also to prove the congruence $W(1,k) = 4+(-1)^k\pmod{8}$ for $k\geq 3$.File in questo prodotto:
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