Let x_n be the n-th non-square positive integer. Thus x_1=2, x_2=3, x_3=5, x_4=6, etc. For a positive real number x, denotes the integer closest to it by \langle x\rangle. If x=m+0.5, where m is an integer, then define \langle x\rangle=m. For example, \langle 1.2\rangle =1, \langle 2.8 \rangle =3, \langle 3.5\rangle =3. Show that x_n=n+\langle \sqrt{n}\rangle