erdos_845

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 $0$? van Doorn and Everts \cite{vDEv25} have disproved this with $C=6$ - in fact, they prove that all integers can be written as such a sum in which $b_t<6b_1$.

theorem erdos_845 :
    answer(False) ↔
      ∀ᵉ (C : ℝ) (hC : 0 < C),
        let f : ℕ × ℕ → ℕ

Recent Submissions

No submissions yet. Be the first to attempt this problem.