Erdős problem 1212

Let $G$ be the graph with vertex set those pairs $(x,y)\in \mathbb{N}^2$ with $\mathrm{gcd}(x,y)=1$ , in which we join two vertices if the differ in only one coordinate, and there by $\pm 1$ .

Sources

The source's own material, retained exactly.

8 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

1212.lean

Retained formal statement4 of 8

Isolation lemma, left neighbour.

FormalConjectures/ErdosProblems/1212.leanErdos1212.left_neighbor_witness_free2 linesExact file

1∀ {P : Finset ℕ} {x y : ℕ},2  (∀ p ∈ P, Nat.Prime p) → 1 ≤ x → (∀ p ∈ P, p ∣ x) → (∀ p ∈ P, ¬p ∣ y) → ∀ p ∈ P, ¬p ∣ x - 1 ∧ ¬p ∣ y

APIStatement only, no proof