# Thread: Find Next Integer

1. ## Find Next Integer

Hi;

I am given the following:

1! + 1 = 2
2! + 1 = 3
4! + 1 = 25
6! + 1 ...
10! + ...
12! + ...
??! + 1 = ...

Find ??. Find the next 5 in the sequence.

Thanks.

2. Originally Posted by Ideasman
Hi;

I am given the following:

1! + 1 = 2
2! + 1 = 3
4! + 1 = 25
6! + 1 ...
10! + ...
12! + ...
??! + 1 = ...

Find ??. Find the next 5 in the sequence.

Thanks.
Quite ironic- we were mentioning this in my number theory class.

Are you familiar with Wilson's Theorem?

16!
18!
22!
28!
30!
36!

And so forth.

The theorem states:

(p - 1)! + 1 is divisible by p, where p is prime. It can proven with minimal effort, too, should you want me to give a proof.

3. I do not think it is a question about Wilson's theorem it is about just finding the next number.

4. Originally Posted by ThePerfectHacker
I do not think it is a question about Wilson's theorem it is about just finding the next number.
It's clearly related to Wilson's theorem.

Originally Posted by ThePerfectHacker
it is about just finding the next number.
You think the "+ 1" is there arbitrarily? If they were just looking for the primes (plus 1), they would just have given 1, 2, 4, 6, 10, 12, ..., p + 1.