Question

4. (a) [3] Let p be prime and let M, denote the number 2P – 1. The number M, is called a Mersenne number, and if it is prime, it is called a Mersenne prime. There is a test, called the Lucas-Lehmer Test, that gives a necessary and sufficient condition for My to be prime. It is always used to verify that a Mersenne number, suspected of being prime, is indeed a Mersenne prime. Give the statement of this test. Why is it a "fast" test for verifying primality? (Look it up in a book or on the internet.) (b) [2] Let p and q be odd primes. There is a necessary condition for q to divide M, found by Fermat (one part) and Euler (the other part). State this condition. Follow the advice in (a).

Answer 1

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