Question

If P₁ and P₂ are two odd prime numbers such that P₁ > P₂ , then P₁2 -P₂2 is …………….. 

A) an even number

B) an odd number

C) a prime number

D) an odd prime number

Answer 1

Correct option is (A) an even number

Given that \(P_1\) and \(P_2\) are two odd numbers such that \(P_1>P_2.\)

Let \(P_1\) = 2m+1 and

\(P_2\) = 2n+1

Then m > n \((\because P_1>P_2)\)

Now, \(P_1^2-P_2^2\) \(=(2m+1)^2-(2n+1)^2\)

\(=(4m^2+4m+1)-(4n^2+4n+1)\)

\(=4(m^2-n^2)+4(m-n)\)

= 4 (m-n) (m+n+1)

\(\therefore\) 4 divides \(P_1^2-P_2^2\)

\(\therefore\) 2 divides \(P_1^2-P_2^2\)

Thus, \(P_1^2-P_2^2\) is an even number.

Answer 2

Correct option is A) an even number