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Math Help - Find Next Integer

  1. #1
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    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.
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  2. #2
    Senior Member
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    Quote Originally Posted by Ideasman View Post
    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.
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  3. #3
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    I do not think it is a question about Wilson's theorem it is about just finding the next number.
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  4. #4
    Senior Member
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    Quote Originally Posted by ThePerfectHacker View Post
    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.

    Quote Originally Posted by ThePerfectHacker View Post
    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.
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