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Question

If p1 and p2 are two odd prime numbers such that p1>p2, then p21p22

A
An even number
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B
An odd prime number
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C
An odd number
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D
A prime number
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Solution

The correct option is A An even number
Let the two odd prime numbers p1 and p2 be 7 and 5 respectively.
Then, p21=72=49
and, p22=52=25
So, p21p21=4925=24 which is an even number.
Take another examples with p1 and p2 be 17 and 13.
Then, p21=172=289
and, p22=132=169
So, p21p21=289169=120 which is an even number.
In general the square of odd prime number is odd.
Hence, the difference of square of two prime numbers is even.
So, A is the correct option.

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