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Question

# If p1 and p2 are two odd prime numbers such that p1>p2, then p21âˆ’p22

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 numberLet the two odd prime numbers p1 and p2 be 7 and 5 respectively.Then, p21=72=49and, p22=52=25So, p21−p21=49−25=24 which is an even number.Take another examples with p1 and p2 be 17 and 13.Then, p21=172=289and, p22=132=169So, p21−p21=289−169=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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