Question

Prove that the square of an any positive integer is of the form 5q,5q+1 ,5q+4 where q is some integer.

Answer 1

By Euclid's division lemma, we have
a=bq+r( where 0<=r<b)
so here let us assume b as 5
hence, a=5q+r(r=0, 1, 2, 3, 4)
if r is 0
a=5q
a^2=25q^2=5(5q^2)=5q(where q=5q^2)
similarly,we can do with r=1, 2, 3&4..

Answer 2

Answer:

here is the best answer in the pic