The number of points with integral coordinates that are interior to the circle x2+y2=16  is

The number of points is equal to the number of integral solutions (x,y)  such that x2+y2<16. So x,y  are integers such that −3≤x≤3, −3≤y≤3  satisfying the inequation x2+y2<16. The number of selections of values is 7, namely –3, –2, –1, 0, 1, 2, 3.The same is true for y. So the number of ordered pairs (x,y)  is 7×7 .But (3,3),(3,−3),(−3,3),(−3,−3)  are rejected because they do not satisfy the inequation x2+y2<16. So, the number of points is 45.