Erdős problem 123 · problems.science

Let $a,b,c>1$ be pairwise coprime integers. Is every large integer a sum of distinct numbers of the form $a^k b^l c^m$ ( $k,l,m\ge 0$ ), none dividing another?

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5 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

123.lean

Retained formal statement4 of 4

In [Er92b] Erdős makes the stronger conjecture (for $a=2$ , $b=3$ , and $c=5$ ) that, for any $\epsilon>0$ , all large integers $n$ can be written as the sum of distinct integers $b_1<\cdots <b_t$ of the form $2^k3^l5^m$ where $b_t<(1+\epsilon)b_1$ .

FormalConjectures/ErdosProblems/123.leanErdos123.erdos_123.variants.powers_2_3_5_snug6 linesExact file

1sorry ↔2  ∀ ε > 0,3    ∀ᶠ (n : ℕ) in Filter.atTop,4      ∃ A,5        ↑A ⊆ ↑(Submonoid.powers 2) * ↑(Submonoid.powers 3) * ↑(Submonoid.powers 5) ∧6          Erdos123.IsSnug ε A ∧ ∑ x ∈ A, x = n

OpenStatement only, no proof

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