Question

If p1 and p2 are two odd prime number such that p1>p2 , then p1 2- p2 2 is

Answer 1

We can pick three sets of numbers:

7 and 5......then  7^2 - 5^2 = 49 - 25 = 24

3 and 1......then 3^2 - 1^2 =  9- 1    =  8

5 and 3......then 5^2 - 3^2  =  25- 9  =16

Therefore from these few examples, we can if the answer will always be an even number

Answer 2

Let p1 = 2n+1 and p2=2n-1. These are odd numbers, for any odd number is given by 2n+1 or 2n-1.

 

Therefore, p12-p22 = (p1+p2) (p1-p2), as you know that a2-b2 = (a+b) (a-b)

 

Substituting the values of p1 and p2 in the above equation, we get

 

p12-p22 = (2n+1+2n-1) (2n+1-2n+1) = 4n * 2 = 8n

 

Thus, p12-p22 is always even, for any n.