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Thread: Modulus proof involving least positive residues

  1. #1
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    Modulus proof involving least positive residues

    I'm a bit stuck on this question:
    Let p be a prime number. Prove that (2p−1)(2p−2)иии(p + 1) ≡−1(mod p).
    Hint: find the least positive residues of 2p−1,2p−2,...,p + 1 (modulo p).
    I think the least positive residues are {0,1,2,...,p} but not entirely sure, and I don't see how it's going to help me answer the question below. Thanks, Alex
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    Re: Modulus proof involving least positive residues

    The least positive residues are 1,2,3,...,p-1 giving

    (p-1)! = -1 (mod p)

    Wilson's Theorem
    Last edited by Idea; Oct 17th 2016 at 04:54 AM.
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    Re: Modulus proof involving least positive residues

    Thanks for replying!
    How do you work out the least positive residues?
    It's a 4 mark question so I think I need to show all my working
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    Re: Modulus proof involving least positive residues

    So you've come to the answer by applying discrete math? Won't the usage of Fermat's Little Theorem solve the problem as well?
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  5. #5
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    Re: Modulus proof involving least positive residues

    How would Fermat's Little Theorem help?
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