Exams › SSC CGL (Prelims) › General

If n is an even number, by which of the following is (8^n - 1) always divisible?

1. 8
2. 65
3. 42
4. 63

Correct answer: 63

Solution

8^n - 1 = (8^2)^(n/2) - 1 = (64)^(n/2) - 1. Since (a^k - 1) is always divisible by (a - 1), we get (64 - 1) = 63 as a factor. Hence 63 always divides 8^n - 1 when n is even.

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