The Erdős–Straus Conjecture

Claim: for every integer n ≥ 2, there exist positive integers x, y, z with 4/n = 1/x + 1/y + 1/z.

Generalises the ancient Egyptian preference for unit fractions; the analogous 2/n statement was settled by Takenouchi and the 3/n case by Mordell (positive). Verified astronomically far (Elsholtz et al., past \(10^{17}\)); equivalent reductions show it suffices to check primes in certain residue classes. The obstruction feels like the Collatz of Diophantine analysis: local flexibility everywhere, global proof nowhere.