Question

euclid division algorithm to prove square of positive integer equal to 3m

Answer 1

Let b=3

a=bq +r

a=3q+r

Possibility of r =0,1,2

1st case:

When r=0

a^2=(3q+0)^2

a^2=9q

a^2=3*3q

Let 3q =m

a^2=3m

2nd case :

When r =1

a^2=(3q+1)^2

a^2=(9q^2+1+2*3q*1)

a^2=(9q^2+1+6q)

a^2=(9q^2+6q)+1

a^2=3(3q^2+2q)+1

Let (3q^2+2q)=m

a^2=3m+1

Hey mate I hope this will help