Question Detail
Question
Use the principle of mathematical induction to determine for which value of k the expression 2^n + 3^n is divisible by k for odd positive integers n.
Correct Answer
Option A is the correct answer.
Detailed Explanation
For odd n, 2^n ≡ 2 (mod 5) and 3^n ≡ 3 (mod 5). Thus, 2^n + 3^n ≡ 2 + 3 ≡ 0 (mod 5), meaning it is divisible by 5. Testing values like n=1 and n=3 confirms this pattern.
Hint
Check the expression modulo 5 and observe what happens when n is odd.