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Factorization of integers

  1. May 23, 2014 #1
    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. jcsd
  3. May 23, 2014 #2

    SteamKing

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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 n-digits, 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
     
  4. May 25, 2014 #3

    Stephen Tashi

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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?
     
  5. May 25, 2014 #4

    PeroK

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    Much of Internet security uses Public Key Cryptography, which depends on large integer factorisation. See, for example:

    http://en.wikipedia.org/wiki/Public-key_cryptography
     
  6. May 25, 2014 #5
    If you want to solve a quadratic equation by factorisation the you need to be able to factorises integers.
    That is to solve

    ax2 + bx + c = 0

    you need to factorises a and c.
     
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