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Erdős problem 1212

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Let GG be the graph with vertex set those pairs (x,y)∈N2(x,y)\in \mathbb{N}^2 with gcd(x,y)=1\mathrm{gcd}(x,y)=1, in which we join two vertices if the differ in only one coordinate, and there by ±1\pm 1.

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The source's own material, retained exactly.

8 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

1212.lean

Retained formal statement3 of 8

Core of the composite-anchor reduction: horizontal-leg vertices (s,c)(s, c) for a≤s≤ba \le s \le b are valid, given the anchor cc is composite and coprime to the whole leg.

FormalConjectures/ErdosProblems/1212.leanErdos1212.horizontal_leg_valid2 linesExact file
∀ {a b c : ℕ},  c.Composite → 2 ≤ a → (∀ (s : ℕ), a ≤ s → s ≤ b → s.gcd c = 1) → ∀ (s : ℕ), a ≤ s → s ≤ b → Erdos1212.Valid (s, c)
APIStatement only, no proof