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    If a and b are two odd prime numbers such that a > b, then a² − b² is:
    Question

    If a and b are two odd prime numbers such that a > b, then a² − b² is:

    A.

    a prime number

    B.

    an odd prime number

    C.

    an odd number

    D.

    an even number

    Correct option is D

    Given:

    a and b are odd primes, so both are odd numbers.

    Concept used:
    Difference of squares:
    a² − b² = (a − b)(a + b)

    Solution:
    Since both a and b are odd,
    → (a − b) is even,
    → (a + b) is even.

    Hence, (a − b)(a + b) = even × even = even number.

    Correct answer is (d) an even number.

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