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Factorization of integers 
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#1
May2314, 08:30 AM

P: 153

Why is factorization of integers important on a first number theory course? Where is factorization used in real life? Are there examples which have a real impact? I am looking for examples which will motivate students.



#2
May2314, 08:47 AM

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I'll take a stab.
Factorization helps determine if a given integer is prime, and one use for prime integers is in devising cryptography keys, which are used quite a bit for, among other things, encrypting sensitive data which might be swapped around on the internet. (NSA, how'm I doin' so far?) If you have an arbitrary integer of ndigits, how long does it take to determine the factors (if any) of this integer? That's a pretty basic question for number theory to answer. Is it a couple of hours, a couple of days, a couple of years, a couple of centuries, or what? Can a better (= quicker) algorithm be devised? http://en.wikipedia.org/wiki/Factorization 


#3
May2514, 09:58 AM

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Suppose we can motivate an interest in Diophantine equations. Their solution entails finding greatest common divisors. Would that also lead in a natural way to focusing on prime numbers?



#4
May2514, 10:16 AM

P: 354

Factorization of integers
http://en.wikipedia.org/wiki/Publickey_cryptography 


#5
May2514, 12:12 PM

P: 33

If you want to solve a quadratic equation by factorisation the you need to be able to factorises integers.
That is to solve ax^{2} + bx + c = 0 you need to factorises a and c. 


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