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kingwinner
#40
Jan11-10, 01:29 AM
P: 1,270
Quote Quote by Petek View Post
If d is a prime, we're done. If d is not prime, then ... . (Do you know the "fundamental theorem of arithmetic"? If not, look it up on Wikipedia,)

Petek
OK, I looked it up on Wikipedia and that theorem says that every integer greater than 1 can be uniquely factored into primes.

If we assumed that d is prime that divides both n! + 1 and (n + 1)! +1 and reached a contradiction, this means that no prime divides both n! + 1 and (n + 1)! +1.

But still, why does it follow that
"No prime divides both n! + 1 and (n + 1)! +1 => no integer greater than 1 divides both n! + 1 and (n + 1)! +1" ?

(sorry, I am very new to number theory and many things do not seem so obvious to me...)

Thanks for explaining!