2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102190The f-invariant is an injective homomorphism from the 2-line of the Adams-Novikov spectral sequence to a group which is closely related to divided congruences of elliptic modular forms. We compute the f-invariant for two infinite families of beta-elements and explain the relation of the arithmetic of divided congruences with the Kervaire invariant one problem.minor changes; final version, to appear in Amer. J. MathAlgebraic Topology55Q10, 55T15, 55N34, 11F33text