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Math Help - find the least positive residue

  1. #1
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    Angry find the least positive residue

    find the least positive residue of (2^(p+1)) + (p-1)! modulo p if p>3 is prime
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  2. #2
    Super Member PaulRS's Avatar
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    By Fermat's Little Theorem we have: 2^{p+1}\equiv{4}(\bmod.p)

    And by Wilson's Theorem: (p-1)!\equiv{-1}(\bmod.p)

    Thus: 2^{p+1}+(p-1)!\equiv{3}(\bmod.p)
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