2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153822We argue the integrability of the generalized KdV(GKdV) equation using the Painlevé test. For $d( \le 2)$ dimensional space, GKdV equation passes the Painlevé test but does not for $d \geq 3$ dimensional space. We also apply the Ablowitz-Ramani-Segur's conjecture to the GKdV equation in order to complement the Painlevé test.7 pages, LaTeXExactly Solvable and Integrable Systemstext