Question Detail
Question
Use principle of mathematical induction to find the value of k, where for all positive integers n, 2^(6n) + 3^(2n-2) is divisible by k.
Correct Answer
Option A is the correct answer.
Detailed Explanation
For n=1: 2⁶ + 3⁰ = 64 + 1 = 65, divisible by 5 and 13. For n=2: 2¹² + 3² = 4096 + 9 = 4105, 4105/5 = 821, divisible by 5. For n=3: 2¹⁸ + 3⁴ = 262144 + 81 = 262225, 262225/5 = 52445. So it appears divisible by 5.
Hint
Test with small values of n to find the common divisor.