Lax Lean Archive

Proof of `The determinant of the least-common-multiple matrix` (3rd statement)

groundedproofs/Lax426240Proofs/LcmDeterminant.lean · lax-426240

What this proof establishes

no assumptions

thm✓Lax426240.LcmDeterminant (3rd statement)

Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.

Read the Lean proof on GitHub

Description

Reindex the antidiagonal sum by the divisor aa: 1/(n/a)=a/n1/(n/a) = a/n, so g(n)=(1/n)∑a∣nμ(a)a=(1/n)∏p∣n(1−p)g(n) = (1/n) ∑_{a ∣ n} μ(a) a = (1/n) ∏_{p ∣ n} (1 − p).