Collatz Conjecture and IMO 1988 Problem 6: Unsolved Dynamics and Perfect Square Link — E8 Intelligence Research

FINDING: The Collatz Conjecture (3n+1) is the most prominently featured unsolved problem, with the "hardest test problem" (IMO 1988 Problem 6) as a secondary focus. | MATH: Collatz map: f(n) = n/2 if n even, 3n+1 if n odd. No closed-form solution; known to hold for n < 2^68 (verified computationally). IMO P6: a,b positive integers with ab+1 | a²+b² ⇒ (a²+b²)/(ab+1) is a perfect square. | CONNECTION: Collatz dynamics exhibit no known modular or geometric symmetry; the IMO P6 solution involves Vieta jumping, which maps to a descent on a lattice of integer pairs — a discrete analogue of a root system reflection (A₁×A₁ type). No golden-ratio or base-60 link in either. | DEPTH: 4 — Collatz is a famous open problem but yields no new constants or harmonic structure; IMO P6 is solved and elegant but not profound for universal geometry. FINDING: "The Oldest Unsolved Problem in Math" — likely the odd perfect number problem or the infinitude of perfect numbers (Euclid-Euler form). | MATH: Even p Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com