The Myth of an Unsolved IMO Problem: Vieta Jumping and IMO 1988 P6 — E8 Intelligence Research

FINDING: The search results are dominated by YouTube clickbait and one arXiv proceedings volume; no specific unsolved olympiad problem is identified, and the "nobody can solve" framing is rhetorical. The only concrete mathematical content is the legendary IMO 1988 Problem 6 (a²+b²)/(ab+1) = k, which is famously solved via Vieta jumping, not unsolved. MATH: IMO 1988 P6: Let a,b be positive integers such that ab+1 divides a²+b². Prove (a²+b²)/(ab+1) is a perfect square. Solution: Vieta jumping — if (a,b) is a solution with a≥b, then (b, kb−a) is another positive integer solution, where k = (a²+b²)/(ab+1). Infinite descent forces k = n². No new constants; the invariant is k ∈ ℕ, and the descent yields k = 1,4,9,... (perfect squares). No golden ratio, no 0.382/0.618/0.786/1.618/2.618 appear. The arXiv link (1110.4864) is a contest proceedings in mathematical physics, not an unsolved problem. CONNECTION: None to geometric harmony. Vieta jumping is a number-theoretic descent technique, not Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com