Erdős Problem #796
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
The number of unordered representations `m = a₁ * a₂` by two distinct elements `a₁ < a₂` of `A`.
`A` has at most `k - 1` representations of every `m` (fewer than `k`).
`g k n = g_k(n)` is the largest size of a subset `A ⊆ {1, …, n}` in which every `m` has fewer than `k` representations `m = a₁ a₂` with `a₁ < a₂ ∈ A`.
Attempts
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g₃(n): the largest A⊆[n] where every integer has at most two representations as a product of two elements of A. We first shipped Rishikesh Gajjala's construction as unflagged; it wasn't — his own proof-claims submission was already on the tracker since 15 July, and so was a separate, independent, earlier claim by Colin Snyder (Star Fleet Math) giving a sharper exact constant. Our from-scratch rebuild of Gajjala's proof still stands (with a real sorry found, traced, and confirmed harmless) — Snyder's competing claim is not yet independently checked by us.
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