Let $C > 0$. Is it true that the set of integers of the form $n = b_1 + \cdots + b_t$, with $b_1 < \cdots < b_t$, where $b_i = 2^{k_i}3^{l_i}$ for $1 \leq i\leq t$ and $b_t \leq Cb_1$ has density $0$?

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

1False ↔2  ∀ (C : ℝ),3    0 < C →4      have f := fun x =>5        match x with6        | (k, l) => 2 ^ k * 3 ^ l;7      {x | ∃ B, ∃ (h : B.Nonempty) (_ : ↑(B.sup f) ≤ C * ↑(B.inf' h f)), ∑ x ∈ B, f x = x}.HasDensity 0

Reported activity

Reported by these sources. Not reviewed here.

• Formalization

  Erdős AI contributions wiki · 8 Jan, 2026 (one form of result), 21 Jan, 2026 (second form)

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  Aristotle

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