# hw04 - What can you say about whether the other one is...

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Math 55: Discrete Mathematics, Fall 2008 Reading and Homework Assignment 4 Reading: Lecture 13: Supplementary notes on Factoring Algorithms Homework (due Monday, 9/29): Odd-numbered self-checking exercises: 3.7: 31, 33, 45, 47, 59 Problems to hand in: 3.7: 32, 46, 60 (A) In Exercise 46, also ﬁnd the decryption exponent d and check that the ﬁrst block of your encrypted message decrypts to the right thing using this expo- nent. (B) Apply Miller’s test to the base 2 (as discussed in 3.7 Exercise 30 and the lecture) to determine that one of the two numbers 1601, 1729 is composite.
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Unformatted text preview: What can you say about whether the other one is prime? (C) Use Pollards algorithm, with f ( x ) = x 2 + 2, and starting value y = z = 6, to factor 17741. (D) (i) Prove that 2 n + 1 is a pseudo-prime to the base 2 if and only if n is a power of 2, and deduce that if 2 n + 1 is prime, then n must be a power of 2. (ii) Verify that 2 1 + 1, 2 2 + 1, 2 4 + 1, 2 8 + 1, and 2 16 + 1 are prime, but that 641 is a factor of 2 32 + 1. Reminder: The rst midterm exam is Friday, Oct. 3. The exam will cover the material on homework assignments 1 through 4....
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