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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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Some Thoughts a start | Comment 1 of 3

let n+2=A and let n!-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
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