Question

prove that the square of any positive integer of the form 7q + 1 is of the same form

Answer 1

We will use Euclid division Lemma here

The Lemma is : If an integer A is divided by B, we get the Quotient Q and Remainder R, which can be written in the form as

A = B Q + R

→0 ≤ R < B

Now, coming to question ,If P is any positive integer, then

P= 1,2,3,4,5,6.........

Let, W=P²= 1,4,9,16,25,36,49,64,.......

W when divided by 7,gives remainder 1, 2 ,4.

So, W can be written in the form:

W= 7 q +1, or 7 q + 2,or 7 q + 4.

So, we can say that , square of any positive integer of the form 7 q + 1 is of the same form as  7 q + 2,or 7 q + 4.

Answer 2

Answer: Jai Shree Mahakaal

Step-by-step explanation:see question 13

Hope it helps