Register to reply 
Factorization of integers 
Share this thread: 
#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

Emeritus
Sci Advisor
HW Helper
Thanks
PF Gold
P: 6,471

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

Sci Advisor
P: 3,283

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: 378

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


#5
May2514, 12:12 PM

P: 35

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. 


Register to reply 
Related Discussions  
Let a, b be positive coprime integers. Show that if two positive integers x, y sat...  Calculus & Beyond Homework  0  
A≡b mod n true in ring of algebraic integers => true in ring of integers  Linear & Abstract Algebra  4  
A^Tx=b given LU factorization for A  Calculus & Beyond Homework  0  
How do I factorize (x1)(x2)(x3)(x4) 48  Precalculus Mathematics Homework  7  
Factorization and 4  Linear & Abstract Algebra  6 