Question

09
Use division algorithm to show that the square of any positive integer is ofthe form
3p or 3p+1.
cricofthe forme​

Answer 1

Hope it helps you!!

Let the positive integer-a

b-3

If b - 3 so

0</= R < b

R =0, 1,2

q= some integer

By using division algorithm

let r =0

a=bq+r

a =3q + 0

a=3q

squaring both side

a^ =(3q) ^

a^= 9q^

a^=3(3q^)

let P= 3q^

a^ = 3P ____________1

Let r = 1

a=bq+ r

a= 3q + 1

squaring both side

a^= (3q+1) ^

a^=(3q)^ + (1) ^ + 2 ×3q×1

a^ =9q^ +1+6q

a^= 9q^+6q+1

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

let 3q^+2q = P

a^=3p+1________________2

From eq 1 and 2 we can say that the square of any positive integer is in the form of 3q and 3q+1 .

But if you are a cbse student ,then you must know that this part is removed from exam point of view.

Thankyou