My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum

LinkBack Thread Tools Display Modes
August 25th, 2013, 03:36 PM   #1
Joined: Aug 2013

Posts: 1
Thanks: 0

Factorial and primes

Does anybody where can I find the proof of the following:

Let (n,k) be the standard combination (choose k among n). Then if

(n,1)=(n,2)=...=(n,n-1)=0 (mod p),

then n=p^t for a non-zero integer t, where p is a prime.

roxy_roller is offline  
August 29th, 2013, 09:10 AM   #2
Senior Member
Joined: Feb 2012

Posts: 628
Thanks: 1

Re: Factorial and primes

It's fairly easy to prove the contrapositive (hence proving the original statement). Suppose that n has a factor other than p. Then would not be divisible by p, since the denominator would have the same number of factors of p as the numerator. And if n is less than p, then it is obvious that no combination of n objects would be divisible by p since p would not appear in the numerator or denominator.
icemanfan is offline  

  My Math Forum > College Math Forum > Number Theory

factorial, primes

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
primes and twin primes: Number between powers of 10 caters Number Theory 67 March 19th, 2014 04:32 PM
factorial tahir.iman Algebra 9 December 26th, 2012 06:22 PM
Sum based on number of primes in a factorial oasawant Number Theory 6 October 25th, 2012 06:25 AM
factorial sum panky Algebra 1 November 29th, 2011 12:31 AM
zero factorial (why ??) sangfroid Number Theory 8 September 15th, 2008 04:28 AM

Copyright © 2019 My Math Forum. All rights reserved.