Question

prove that the square of any positive integer of the form 5m+1 will leave a reminder 1 when divided by 5 for some integer m​

Answer 1

when,r=0 then a=5q+0

r=1. a=5q+1

now(5a)^2=5(5q)^2 then (5q^2) is m

=5m

(5q+1)^2=25q^2+10q+1

5(5q^2+2q)+1

5m+1.