Divisibility of Exponential Difference

CAT 2002 Slot 1 · QA · Medium · Number System

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76n−66n7^{6n} - 6^{6n}, where nn is an integer >0> 0, is divisible by:

  1. A.

    13

  2. B.

    127

  3. C.

    559

  4. D.

    All of these

Answer

D

Explanation

For n=1n = 1, 76−66=(73−63)(73+63)=(343−216)(343+216)=127×5597^6 - 6^6 = (7^3 - 6^3)(7^3 + 6^3) = (343 - 216)(343 + 216) = 127 \times 559. Also, 559=13×43559 = 13 \times 43. Thus, 76n−66n7^{6n} - 6^{6n} is divisible by 1313, 127127, and 559559. Hence, 'All of these' is the correct answer.

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