Unformatted text preview: b ) p = a p + b p modulo p ). Problem 3 At some point, long ago, people seeking prime numbers had hoped that many integers of the form 2 n1 (socalled Mersenne numbers) would be prime. It’s true for n = 2 , 3 but not n = 4. Prove that if n > 2 is not a prime number then 2 n1 is not a prime either. Problem 4 Consider the Fibonacci numbers: F = 0, F 1 = 1, F n = F n1 + F n2 , for n > 1. Show how to compute F n using only O (log n ) additions and multiplications. (Hint: express the recurrence as a twobytwo matrix.)...
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 Fall '07
 CharikarandChazelle
 Computer Science, Natural number, Prime number, Mersenne prime

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