2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228059We consider the ternary Goldbach problem with two prime variables of the form $k^2+m^2+1$ and find an asymptotic formula for the number of its solutions.Number Theory11N13; 11N36; 11P32The ternary Goldbach problem with arithmetic weights attached to two of the variablestext