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 statement8 of 8

Isolation lemma, vertical neighbours: both coordinates even.

FormalConjectures/ErdosProblems/1212.leanErdos1212.vertical_neighbor_both_even1 lineExact file

1∀ {x y : ℕ}, 2 ∣ x → ¬2 ∣ y → (2 ∣ x ∧ 2 ∣ y + 1) ∧ (1 ≤ y → 2 ∣ x ∧ 2 ∣ y - 1)

APIStatement only, no proof