4383_Notes_3o1_fill2

4383_Notes_3o1_fill2 - Math 4383 Section 3.1 Page 1 of 6...

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Math 4383 Section 3.1 Page 1 of 6 Number Theory Section 3.1 The Fundamental Theorem of Arithmetic A prime is a positive integer p > 1 with the property that the only positive divisors of p and 1 and p itself. A positive integer > 1 is called composite if it is not prime. Smallest primes – 2, 3,5, 7, 11, 13, 17, 19, … Why primes? Answer: positive composite integer can be written as a product of prime integers, and the factoring is unique up to the order of the factors. Notice that none of the divisibility material we discussed in Chapter 2 needed the concept of a prime number, but to go further in number theory, primes are essential. Let’s start with the following basic consequences of the definition of a prime number: Theorem: If p is a prime number and p|ab, then either p|a or p|b. Proof:
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4383_Notes_3o1_fill2 - Math 4383 Section 3.1 Page 1 of 6...

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