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Math Help - Let p be odd. Then 2(p-3)!\equiv -1 (mod p)

  1. #1
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    Let p be odd. Then 2(p-3)!\equiv -1 (mod p)

    Let p be odd. Then 2(p-3)!\equiv -1 \ \mbox{(mod p)}

    Don't know how to do this one.
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by dwsmith View Post
    Let p be odd. Then 2(p-3)!\equiv -1 \ \mbox{(mod p)}

    Don't know how to do this one.
     2(p-3)!=(-1)(-2)(p-3)!\equiv(p-1)!\equiv-1\bmod{p}
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  3. #3
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    Quote Originally Posted by chiph588@ View Post
     (-1)(-2)(p-3)!\equiv(p-1)!
    How do you show those two are congruent though?
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  4. #4
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by dwsmith View Post
    How do you show those two are congruent though?
     p-a\equiv-a\bmod{p}
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  5. #5
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    Quote Originally Posted by chiph588@ View Post
     p-a\equiv-a\bmod{p}
    I don't see the connection.
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  6. #6
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by dwsmith View Post
    I don't see the connection.
    What are you having trouble with?
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