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  1. It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
    2. A.

    (216 + 1)
    B.

    (216 - 1)
    C.

    (7 x 223)
    D.

    (296 + 1)

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    Answer : Option D

    Explanation :

    Let 232 = x. Then, (232 + 1) = (x + 1).

     

    Let (x + 1) be completely divisible by the natural number N. Then,

     

    (296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.

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