Question Detail
Question
The statement 3^(2n) - 1 is divisible by which of the following?
Correct Answer
Option C is the correct answer.
Detailed Explanation
For n=1: 3² - 1 = 9 - 1 = 8, divisible by 8. For n=2: 3⁴ - 1 = 81 - 1 = 80, divisible by 8 (80/8=10). For n=3: 3⁶ - 1 = 729 - 1 = 728, 728/8 = 91. It appears 3^(2n) - 1 is always divisible by 8. This can be proven by induction or using the fact that 3^(2n) = 9ⁿ and 9 ≡ 1 mod 8, so 9ⁿ ≡ 1 mod 8.
Hint
Test with small values of n to find a pattern.