All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Factors and Primes (Posted on 2007-01-24) Difficulty: 3 of 5
Prove that n!-1 is a composite number when n>3 and n+2 is a prime.

No Solution Yet Submitted by atheron    
Rating: 4.6667 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts a start | Comment 1 of 3

let n+2=A and let n!-1=B

n=A-2

(A-2)!-1=B

(1)    (A-2)!=B+1

now let P1,P2,....,Pk be all the primes less than or equal to A-2

now from (1) be get that B+1 is divisible by all of P1,P2,...,Pk thus B is congruent to (Pk-1) mod Pk for all Pk

this is where I am stuck, if anybody can offer some assistance I would greatly appreciate it.

My instincts tell me that B+1 being divisible by a bunch of consecutive primes forces B to be composite but I'm having problems proving it


  Posted by Daniel on 2007-01-24 10:34:13
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information