2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166671We globally classify two-component evolution equations, with homogeneous diagonal linear part, admitting infinitely many approximate symmetries. Important ingredients are the symbolic calculus of Gel'fand and Dikii, the Skolem-Mahler-Lech theorem, results on diophantine equations in roots of unity by F. Beukers, and an algorithm of C.J. Smyth.40 pages, 1 figure, submitted to Foundations of Computational Mathematics, with globally complete description of highest degree divisors, corrected typos and added referencesExactly Solvable and Integrable Systemstext