Divisibility of Exponents

CAT 1995 Slot 1 · QA · Easy · Number Systems

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56−15^6 - 1 is divisible by which of the following?

  1. A.

    1313

  2. B.

    3131

  3. C.

    55

  4. D.

    None of these

Answer

B

Explanation

56−1=(53)2−1=(125)2−1=(125−1)(125+1)=124×1265^6 - 1 = (5^3)^2 - 1 = (125)^2 - 1 = (125 - 1)(125 + 1) = 124 \times 126. 124=31×4124 = 31 \times 4. Thus, 56−15^6 - 1 is divisible by 3131.

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