Question Detail
Question
For all k ∈ N, 2^(5k) - 1 is divisible by
Correct Answer
Option E is the correct answer.
Detailed Explanation
2^5 = 32 ≡ 1 (mod 31). Hence, 2^(5k) = (2^5)^k ≡ 1^k ≡ 1 (mod 31). Therefore, 2^(5k) − 1 is divisible by 31 for all k.
Hint
Evaluate 2^5 modulo a number and extend using powers.