Final answer:
The question seeks an appropriate polynomial identity method to check if a number of the form 22k-1 is prime, employing Fermat's Little Theorem.
Step-by-step explanation:
The question is asking which method utilizes a polynomial identity to determine if a number of the form 22k−1 is prime. A famous identity used in this case is Fermat's Little Theorem, which states that if p is prime, then for any integer a such that GCD(a, p) = 1 (they are coprime), it holds that ap-1 ≡ 1 (mod p).
When k is an integer, we have 22k ≡ 1 (mod 2k−1) only if 2k−1 is prime. To verify this, one can raise 2 to the power 2k using the binary exponentiation method and check if the result minus 1 is divisible by 2k−1. If 2k−1 is not prime, the congruence will not hold, indicating a composite number.