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For any integer n greater than or equal to 2, the expression 8ⁿ - 7n - 1 must be divisible by:

1. 64
2. 49
3. 343
4. 7

Correct answer: 49

Solution

8ⁿ = (1+7)ⁿ = 1 + 7n + C(n,2)*49 + (terms with 7³ and higher). So 8ⁿ - 7n - 1 = 49*C(n,2) + 49*(multiples of 7 and higher) = 49*(integer). Hence 8ⁿ - 7n - 1 is always divisible by 49.

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