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Math Help - Proof using wilson's method, I believe

  1. #1
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    Proof using wilson's method, I believe

    How would I prove that 4(29!) + 5! is divisible by 31?
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  2. #2
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    Quote Originally Posted by MichaelG View Post
    How would I prove that 4(29!) + 5! is divisible by 31?

    Modulo 31 we have 4(29!)+5!=\frac{4(30!)}{30}=\frac{4(-1)}{-1}+5!=4+4!\cdot 5=4+24\cdot 5=4+(-7)5=4-35=-31

    Tonio
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