Positive Multiplicative Orbit Strict 3-AP Rigidity
Provedmul_subgroup_positive_ap3_rigidcombinatoricserdos-problemsnumber-theory
For positive real elements u, v > 0 lying on the hyperbola u * v = 1, the arithmetic progression condition 1 + v = 2u uniquely forces u = 1 and v = 1.
Formal statement
import Mathlib
theorem mul_subgroup_positive_ap3_rigid (u v : ℝ) (hu : 0 < u) (hv : 0 < v)
(h_geom : u * v = 1) (h_ap : 1 + v = 2 * u) : u = 1 ∧ v = 1 := by sorry