The number of points with integral coordinates that lie in the interior of the region common to the circle ${\mathrm{x}}^2+{\mathrm{y}}^2=16$ and the parabola ${\mathrm{y}}^2=4\mathrm{x} \mathrm{is}$

$$\begin{gathered} {\mathrm{x}}^2+{\mathrm{y}}^2=16, {\mathrm{y}}^2=4\mathrm{x} \\ 0<\mathrm{x}<4 \\ \left(1\right) \mathrm{x}=1, {\mathrm{y}}^2<4\mathrm{x} \\ {\mathrm{y}}^2<4\Rightarrow \mathrm{y}=-1,0,1 \\ (1,-1),(1,0),(1,1) \to 3 \\ \left(2\right) \mathrm{x}=2\Rightarrow {\mathrm{y}}^2<8\Rightarrow \mathrm{y}=-2,-1,0,1,2 \\ \Rightarrow (2,-2),(2,-1),(2,0),(2,1),(2,2) \to 5 \\ \left(3\right) \mathrm{x}=3\Rightarrow {\mathrm{y}}^2<12\Rightarrow \mathrm{y}=-3,-2,-1,0,1,2,3 \\ (3,-2)(3,-1)(3,0)(3,1)(3,2) \to 5 \\ \mathrm{possible} points satisfies \mathrm{both} \mathrm{are} = 13 \end{gathered}$$