Question

If p₁ and p₂ are two odd prime numbers such that p₁ > p₂, then $p_1^2-p_2^2$ is

(a) an even number
(b) an odd number
(c) an odd prime number
(d) a prime number

Answer 1

Let the two odd prime numbers and be 5 and 3.

Then,

And

Thus,

16 is even number.

Take another example, with and be 11 and 7.

Then,

And

Thus,

72 is even number.

Thus, we can say that is even number

In general the square of odd prime number is odd. Hence the difference of square of two prime numbers is odd

Hence the correct choice is (a).