Question

Prove that the square of any positive integer of the form 5q + 1 is of the same form.

Answer 1

Let "a" be any positive integer.

Let a= 5q + 1

Then $a^2$ = $(5q+1{)}^2$

= 25 $q^2$ + 10 q + 1

= 5q ( 5q +2) +1

= 5m +1 [ m= q( 5q +2) ]

Hence, a is of the form of 5q + 1.