Factorization of integers

  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. SteamKing

    SteamKing 8,626
    Staff Emeritus
    Science Advisor
    Homework Helper

    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
     
    1 person likes this.
  4. Stephen Tashi

    Stephen Tashi 4,318
    Science Advisor
    2014 Award

    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?
     
    1 person likes this.
  5. PeroK

    PeroK 1,088
    Homework Helper
    Gold Member

    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. 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.
     
    1 person likes this.
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?

0
Draft saved Draft deleted