Question

If p₁ and p₂ are two odd prime numbers such that p₁ > p₂, then

\[p_1^2 - p_2^2\]  is

Options

•  an even number

• an odd number

• an odd prime number

• a prime number

Answer 1

Let the two odd prime numbers `p_1` and `p_2`be 5 and 3.

Then,  

`p_1^2=5^2`

=25

and 

`p_1^2-p_2^2=25-9`

`=16`

16 is even number.

Take another example, with `p_1` and `p_2`be 11 and 7.

Then, 

Take another example, with `p_1` and `p_2`be 11 and 7.

Then, 

`p_1^2=11^2`

=121

and 

`p_1^2=7^2`

=49

thus, 

`p_1^2- p_2^2=121-49`

=72

72 is even number.

Thus, we can say that `p_1^2- p_2^2` 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).