  We first investigate properties of M-tensor equations. In particular, we show
that if the constant term of the equation is nonnegative, then finding a
nonnegative solution of the equation can be done by finding a positive solution
of a lower dimensional M-tensor equation. We then propose an inexact Newton
method to find a positive solution to the lower dimensional equation and
establish its global convergence. We also show that the convergence rate of the
method is quadratic. At last, we do numerical experiments to test the proposed
Newton method. The results show that the proposed Newton method has a very good
numerical performance.
