Let M be a point which has coordinates (p×1994,7p×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. analytic geometrygeometryincentercombinatorics unsolvedcombinatorics