
Number Theory Number Theory Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 13th, 2015, 04:46 AM  #1 
Member Joined: May 2014 From: India Posts: 87 Thanks: 5 Math Focus: Abstract maths!  Proof regarding divisibility of factorial by composite numbers.
If N is a composite number greater than 4, prove that: $(N  1)! \equiv 0(mod N)$ 
May 13th, 2015, 04:50 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
Let N = ab with a,b coprime and greater than 1. Then since a and b are both less than N1, both divide (N1)! and hence ab divides (N1)!, as desired. All that's left is for you to handle the case of powers of primes. 
May 13th, 2015, 05:16 AM  #3 
Member Joined: May 2014 From: India Posts: 87 Thanks: 5 Math Focus: Abstract maths!  
May 13th, 2015, 05:50 AM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  
May 13th, 2015, 11:36 PM  #5 
Member Joined: Jul 2014 From: israel Posts: 76 Thanks: 3 
this will help you out Wilson's theorem  Wikipedia, the free encyclopedia Wilson's theorem states that a natural number n > 1 is a prime number if and only if (N−1)!≡1(mod N) Lagrange gave the first proof in 1771 please also check the "Composite modulus" section ... Last edited by isaac; May 13th, 2015 at 11:40 PM. 

Tags 
composite, divisibility, factorial, numbers, proof 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
prime numbers and composite numbers  shaimaa saif  Algebra  10  November 17th, 2015 08:02 AM 
Composite numbers primelike  mobel  Number Theory  24  October 30th, 2014 09:18 AM 
Some rules about composite numbers  Tylerman  Number Theory  26  April 17th, 2012 09:43 PM 
Composite numbers among a formula  butabi  Number Theory  2  October 12th, 2010 12:26 PM 
Factorial for complex numbers?  3hlang  Number Theory  1  June 5th, 2009 11:57 AM 