Question

The square of any positive integer of the form 5q + 1 is of the same form.
If true then enter $1$ and if false then enter $0$

Answer 1

Let x be any positive integer of the form 5q + 1.
When x =5q +1
$x^2=25q^2+10q+1$
$x^2=5q(5q+2)+1$
Let m=q (5q +2).
$x^2=5m+1$
Hence, $x^2$ is of the same form i.e. 5m + 1.