An integer lattice point (or a lattice point) on the xy-plane is a point whose coordinates are both integers. For example, the point (3, –5) is a lattice point but the point (0.5, 0) is not. A triangular region R is bounded by three lines with the following equations: x+y=200, x+3y=0 and 3x+y=0. How many lattice points lie (i) on the boundaries of R? (ii) inside R?
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