2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128354In this short article, we prove that any automorphism of the R. Thompson's group $F$ has infinitely many twisted conjugacy classes. The result follows from the work of Matthew Brin, together with a standard facts on R. Thompson's group $F$, and elementary properties of the Reidemeister numbers.10 pagesGroup TheoryAlgebraic Topology20E45;37C25; 55M20text