CMO 1994 Problem 6

Let $M$ be a point which has coordinates $(p\times 1994,7p\times 1994)$ in the Cartesian plane ( $p$ is a prime). Find the number of right-triangles satisfying the following conditions: (1) all vertexes of the triangle are lattice points, moreover $M$ is on the right-angled corner of the triangle; (2) the origin ( $0,0$ ) is the incenter of the triangle.