2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131959Let g be a cubic polynomial with integer coefficients and n>9 variables, and assume that the congruence g=0 modulo p^k is soluble for all prime powers p^k. We show that the equation g=0 has infinitely many integer solutions when the cubic part of g defines a projective hypersurface with singular locus of dimension <n-10. The proof is based on the Hardy-Littlewood circle method.18 pagesNumber TheoryAlgebraic Geometry11D72; 11P55text