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MATH135 Lecture Notes - Lecture 22: Integer Factorization, If And Only If

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23 Oct 2015

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$MATH135 Full Course Notes$

MATH135 Full Course Notes

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Math 135 - lecture 22: pad, uft, and dfpf. Pad is referred to as a corollary of cad. If p is prime and p | (m1m2,,mn) for integers m1, m2,,mn then p | mi for some mi. There are an infinite number of primes. Also known as the fundamental theorem of arithmetic. If n > 1 is an integer, then n can be written as a product of prime factors and, apart from the order of factors, this factorization is unique. The number of divisors is determined by the exponent on each unique factor (ie. 3 and 7 and raised to the powers of 2 and 1, respectively) So 63 has (2 + 1) (1 + 1) = 6 divisors. We consider negative divisors as well as positive divisors, so 2 * (1 + 1) (2 + 1) = 12 divisors of 2940 are multiples of 12. 3 prove that a2 | b2 iff a | b.

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