7 6 n − 6 6 n , where n is an integer > 0 , is divisible by (CAT 2002) Options: A . &nbsp13 B . &nbsp127 C . &nbsp559 D . &nbspAll of these E . &nbsp81

76n−66n, where n is an integer >0, is divisible by (CAT 2002)

Question

7^{6 n} - 6^{6 n},

where n is an integer

> 0

, is divisible by (CAT 2002)

Answer: Option D
:
D
Ans: (d)
For

n = 1, 7^{6} - 6^{6} = (7^{3})^{2} - (6^{3})^{2};

= (7^{3} - 6^{3}) (7^{3} + 6^{3}) = (343 - 216) (343 + 216); = 127 * 559 = 127 * 13 * 43.

Hence it is divisible by

127, 13, 559.

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