If $A \subset C$ is a finite set and $k \geq 1$ then let $A_{k} = {z_{1} + \dots + z_{k} : z_{i} \in A distinct} .$ For $k > 2$ does the multiset $A_{k}$ (together with the size of $A$ ) uniquely determine the set $A$ ?

Worked, still open.

analysis · solved · formalized (Lean) · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

formal

AMS 5 · solved (literature)

theorem erdos_494.variants.k_eq_2_card_not_pow_two :
    ∀ card : ℕ, (∀ l : ℕ, card ≠ 2 ^ l) → Erdos494Unique 2 card

solved