I. Fermat's test consists of using Fermat's Theorem (an¹=1 (mod n)) with prime n. Just pick any number a E {1, ..., n-1} and check if it satisfies the expression. If not, then it must be a composite number, that is, it is not prime. II. Although Fermat's Theorem is used to check whether a number is prime or not, we can still obtain equality (an¹-1 (mod n)) even when n is not prime. E The numbers for which this situation occurs are called Carmichael numbers or pseudoprimes. III. Both the Miller-Rabin and AKS algorithms (checking a prime number) work for any type of input and are polynomial time. However, only AKS is deterministic. IV. The Miller-Rabin algorithm guarantees when a number is prime, but when it is composite (non-prime) it can only guarantee this characteristic in probabilistic terms. Only the following items are correct: A I, II, III B I, II, IV C I, III, IV D II, III, IV E I, II, III, IV
I. Fermat's test consists of using Fermat's Theorem (an¹=1 (mod n)) with prime n. Just pick any number a E {1, ..., n-1} and check if it satisfies the expression. If not, then it must be a composite number, that is, it is not prime.
II. Although Fermat's Theorem is used to check whether a number is prime or not, we can still obtain equality (an¹-1 (mod n)) even when n is not prime. E The numbers for which this situation occurs are called Carmichael numbers or pseudoprimes.
III. Both the Miller-Rabin and AKS algorithms (checking a prime number) work for any type of input and are polynomial time. However, only AKS is deterministic.
IV. The Miller-Rabin
Only the following items are correct:
A | I, II, III | |
B | I, II, IV | |
C | I, III, IV | |
D | II, III, IV | |
E | I, II, III, IV |
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