Question

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

Answer 1

have a look here is your answer....

Answer 2

we know that, a=bq+r (0<\=r<b)
3m or 3m+1
b=3,r=0,1,2
...
if r =0 so,
a=3q+0
a² =3q²
suppose 3q²=m
so, a² =3m

if R is equals to 1
so a=3q+1
=(3q+1)²
by identity
=3q²+1²+2(3q)
a²=9q²+1+6q +1
take 3 common
=3(3q²+2q)+1
suppose..3q²+2q=m
a²=3m+1


if R is equals to 2
so a=3q+2
=(3q+2)²
=9q²+12q+4
=9q²+12q+3+1
=3(3q²+4q+1)+1
suppose 3q²+4q+1=m
a²=3m+1