GrahamConjecture — Mathlib

English

From an IsNat relation between p and np, LucasLehmerTest np implies LucasLehmerTest p.

Русский

Из отношения IsNat между p и np следует, что LucasLehmerTest(np) влечёт LucasLehmerTest(p).

LaTeX

$$$\text{IsNat}(p, np) \Rightarrow (\text{LucasLehmerTest}(np) \Rightarrow \text{LucasLehmerTest}(p))$$$

Lean4

/-- Statement of Graham's conjecture (which is now a theorem in the literature).

Graham's conjecture states that if $0 < a_1 < \dots a_n$ are integers, then
$\max_{i, j} \frac{a_i}{\gcd(a_i, a_j)} \ge n$. -/
def GrahamConjecture (n : ℕ) (f : ℕ → ℕ) : Prop :=
  n ≠ 0 → StrictMonoOn f (Set.Iio n) → ∃ i < n, ∃ j < n, (f i).gcd (f j) * n ≤ f i

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