Question

prove that square of any positive integer of the form 5m+1 of the same form​

Answer 1

Let n=5m+ 1 where m is a positive integer.

Squaring on both sides

n²=(5m+ 1)²

=25m²+10m+1

=5(5m²+2m)+1

=5q+1, where q is a integer and q=5m²+2m

Hence, the square of any positive integer of the form 5m+1 is of the same form.