Prove that the square of any positive integer is of the form 5q+1 will leave a remainder 1 when divided by 5for some integer m​

let take a and b be the positive integer so , a=bq+r (0<r<b)

so , b = 5 given

remainder = 0,1,2,3 and 4

squaring both sides :

(a) = (5m ka whole square)

a square = 25m square

let take common out

a square = 5(5m square)

so , 5m square = q

a square = 5q