2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75577Given an absolutely irreducible ternary form $F$, the purpose of this paper is to produce better upper bounds for the number of integer solutions to the equation F=0, that are restricted to lie in very lopsided boxes. As an application of the main result, a new paucity estimate is obtained for equal sums of two like powers.15 pages; to appear in Math. ZeitNumber Theory11G35 (11P05)text