Quote by Petek
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!