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