Question

The number of integral points (integrals poems mean both coordinate should should be integers ) exactly with the interiors of triangle with vertices (0,0),(4,3)and(21,0)

Answer 1

The equation of the line joining (0, 21) and (21, 0) is x+y = 21 or y = -x+21. Thus 19, 18, ..., 0 integral points lying inside the triangle at x = 1, 2, ..., 20, respectively. In all, there are 19+18+...+0 = 19(20)/2 = 190 points.