# The Marica-Schönheim special case of Graham's conjecture #

Graham's conjecture states that if $0 < a_1 < \dots a_n$ are integers, then $\max_{i, j} \frac{a_i}{\gcd(a_i, a_j)} \ge n$. This file proves the conjecture when the $a_i$ are squarefree as a corollary of the Marica-Schönheim inequality.

## References #

*Applications of the FKG Inequality and Its Relatives*, Graham

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 $\max_{i, j} \frac{a_i}{\gcd(a_i, a_j)} \ge n$.

## Equations

## Instances For

theorem
Nat.grahamConjecture_of_squarefree
{n : ℕ}
(f : ℕ → ℕ)
(hf' : ∀ k < n, Squarefree (f k))
:

n.GrahamConjecture f

The special case of Graham's conjecture where all numbers are squarefree.