prove that for every integer n there is a integer know such

prove that for every integer n, there is a integer know such that
N^2 +1<k<n^2 +3

Deseret math

n is an integer that is it could be a positive or a negative whole number .

now the square of a negative number is always positive

=> lets say there is a integer k

now if n=1 then n^2 = 1

and n^2+1 = 2

and n^2+3 = 4

so beteen 2 and 4 we have an integer 3 so in this situation k=3

in general we can say that the difference beteen n^2 + 3 and n^2+3 is = (n^2+3) - (n^2+1) = 2

so k will alays lie in beteen n^2+1 and n^2+3

and between (n^2+3) and (n^2+1) there will always be an integer

hence proved that there is a integer known such that
n^2 +1 < k < n^2 +3