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WindowTitle->4. Prime Factorization | Introduction to Number Theory
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development of an easy way to factor large prime numbers.\
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Can you imagine representing integers in a canonical, systematic way? As a \
sum or a product of specific numbers? If we could do it, we then could \
generalize so many things about numbers. We could just examine those little \
bricks that make up the number we want to examine.\
\>", "Text",
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Well, it is quite the reality! It turns out, every number can be represented \
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It turns out, factoring large numbers is a hard task. In fact, secure \
transfers of information (like digital credit card transactions) rely on that \
very fact. Returning to the Bill Gates quote, if we could find an easy way to \
factor large numbers, then the entire system of secure transactions would \
fail.\
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This lesson will be about prime factorization and some things derived from it.\
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Intuitively, that means that every integer is built out of prime numbers. \
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As seen, the primes in the product are neither distinct nor arranged in any \
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A nice representation of prime factorization would be achieved by arranging \
primes in increasing order and associating sets of equal primes into single \
factors:\
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Up until now, there has been no discussion about the uniqueness of such a \
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Obviously, the prime factorization of primes is just themselves because they \
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