Infrared singularities of the gluon propagator and quark confinement in the limit of an infinite number of colors

An exact solution is obtained for the quark propagator in chromodynamics with neglect of the gluon-gluon interaction in the limit $N\to\infty$ for different asymptotic behaviors of the gluon propagator as $k\to 0$. It is shown that a singularity of the type $k^{-2n}$, $n\leqslant 2$, leads to quark confinement.