Let $k (N)$ denote the size of the largest set $A \subseteq {1, \dots, N}$ such that the sets $S_{r} = {a_{1} + \dots + a_{r} : a_{1} < \dots < a_{r} \in A}$ are disjoint for distinct $r \geq 1$ . Estimate $k (N)$ - in particular, is it true that $k (N) \sim 2 N^{1/2}$ ?

Worked, still open.

number theory · solved · possible · 0 attempts

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