Question

show that square of any positive integer is of the form 3m or 3m+1

Answer 1

let us take, 'x'= 3q , 3q+1, 3q+2
when, x=3q
        x2 =  (3q) 2
         x2 = 9q2 
        x2  = 3(3q2)
we see that 3q2= m
so we have done the first equation 3m

when , x=3q+1
           x2= (3q+1)2
                                 [since, (a+b)2 = a2+2ab+b2]
           x2= 9q+6q+1
           x2= 3(3q+2q)+1
in this we see that 3q+2q= m
    therefore, this satisfy the equation m+1

Answer 2

$\textbf{Answer is in Attachment !}$