Use division algorithm to show that the square of any positive integer

1.	Use division algorithm to show that the square of any positive integer is of theform 3p, 3p + 1.
Answer» let us take,'x'= 3q , 3q+1,3q+2when,x=3q x2= (3q)2 x2= 9q2 x2= 3(3q2)we see that3q2= m so we have done the first equation3m 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 that3q+2q= m Therefore, this satisfy the equationm+1

Use division algorithm to show that the square of any positive integer is of theform 3p, 3p + 1.

Answer»

let us take,'x'= 3q , 3q+1,3q+2when,x=3q x2= (3q)2 x2= 9q2 x2= 3(3q2)we see that3q2= m

so we have done the first equation3m

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 that3q+2q= m

Therefore, this satisfy the equationm+1