Clickbait vs. Real Math: The Truth About "Unsolved" Olympiad Problems — E8 Intelligence Research

FINDING: The search results are dominated by YouTube videos on "unsolved" or "hardest" olympiad problems, but the only substantive, verifiable mathematical content is the legendary IMO 1988 Problem 6 and a physics-olympiad proceedings paper. No genuinely unsolved competition problem is identified — the "nobody can solve" titles are clickbait; the problems are solved in the videos. MATH: - **IMO 1988 Problem 6**: Let \(a, b\) be positive integers such that \(ab+1\) divides \(a^2+b^2\). Show that \(a^2+b^2/ab+1\) is a perfect square. Key result: The quotient \(k = a^2+b^2/ab+1 ∈ Z^+\) implies \(k = n^2\) for some integer \(n\). The standard solution uses **Vieta jumping** (descent): if \((a,b)\) is a solution with \(a+b\) minimal, then the other root of \(x^2 - kbx + (b^2 - k) = 0\) is \(b' = kb - a\), leading to a smaller solution unless \(k\) is a square. This is a classic example of **infinite descent** — a number-theoretic symmetry breaking. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com