Question

If p1 and p2 are 2 odd prime no. such that p1 > p2, then p1²-p2² is a)an even no. b)an odd no. c)an odd prime no. d)a prime no.

Answer 1

Answer:

a) an even no.

Step-by-step explanation:

supposep1=5 and p2=3

hence 25-9=16

Answer 2

Answer: a) an even number.

Step-by-step explanation:

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.