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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)

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Solution Solution Comment 3 of 3 |
If n+2 is prime, then by Wilson's theorem
(n+1)! = -1 (mod (n+2))
=> n! = 1 (mod (n+2))
=> n!-1 =0 (mod (n+2))
If (n+2) is prime, then n!-1 is divisible by (n+2)
making n!-1 a composite number.

  Posted by Praneeth on 2007-09-27 06:01:18
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