erdos_172

Specification

Is it true that in any finite colouring of $\mathbb{N}$ there exist arbitrarily large finite $A$ such that all sums and products of distinct elements in $A$ are the same colour?

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Lean 4 Statement

theorem erdos_172 : answer(sorry) ↔
    ∀ (n : ℕ) (color : ℕ → Fin n) (m), ∃ (A : Finset ℕ), A.card ≥ m ∧ ∃ c, ∀ (S : Finset A),
    S.Nonempty → color (∑ x ∈ S, x) = c ∧ color (∏ x ∈ S, x) = c

ID: ErdosProblems__172__erdos_172

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