Question

prove that any perfect square when divided by 4 leaves remainder 1 or 0​

Answer 1

let a^2 be any perfect square no.

then,a is of the form 2q or 2q+1

now,

if a =2q,

a^2 =(2q)^2

=4qq

here, the remainder is zero

again,if a=2q+1

a^2=(2q+1)^2

=4qq+4q+1

=4(qq+q)+1

here the remainder is 1

hence, any perfect square leaves remainder 1or 0 when divided by 4