Erdős problem 1110 · problems.science

Let $p>q\geq 2$ be two coprime integers. We call $n$ representable if it is the sum of integers of the form $p^kq^l$ , none of which divide each other.

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1110.lean

Retained formal statement1 of 1

Let $p>q\geq 2$ be two coprime integers. We call $n$ representable if it is the sum of integers of the form $p^kq^l$ , none of which divide each other.

If $\{p,q\}\neq \{2,3\}$ then what can be said about the density of non-representable numbers? Are there infinitely many coprime non-representable numbers?

FormalConjectures/ErdosProblems/1110.leanErdos1110.erdos_11103 linesExact file

1True ↔2  ∀ (p q : ℕ),3    q < p → 2 ≤ q → p.Coprime q → ¬(p = 3 ∧ q = 2) → {n | n.Coprime (p * q) ∧ ¬Erdos1110.Representable p q n}.Infinite

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