# 3_NumberTheory - Examples Mersenne primes have the form...

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Primes 9/1/11 Theorem 1. Fundamental Theorem of Arithmetic Every positive integer greater than 1 can be written uniquely as a prime or as a product of two or more primes written in the order of nondecreasing size. Examples Definition : Let P be a positive integer greater than 1. p is a prime number if the only positive factors of p are 1 and p. p is a composite number if it has a positive factor other than 1 and itself.

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Theorem 2. Theorems 3&4.

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Unformatted text preview: Examples Mersenne primes have the form Greatest Common Divisor (GCD) Definition : Example Definition : Least Common Multiple (LCM) Example: Example: Theorem 5 . Let a and b be positive integers. Then ab = gcd(a,b)*lcm(a,b). Euclidean Algorithm Proof of Euclidean Algorithm Theorem 6 Lemma 3 Section 4.3, Problem 15' . Find all primes <= 30. Problem 15 . Find all positive integers that are < 30 and relatively prime to 30....
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3_NumberTheory - Examples Mersenne primes have the form...

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