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Fermat's Little Theorem

  1. Apr 3, 2012 #1
    1. The problem statement, all variables and given/known data
    Use Fermat's Little Theorem to calculate 18[itex]^{802}[/itex](mod29)


    2. Relevant equations
    Fermat's Little Theorem: a[itex]^{p-1}[/itex][itex]\equiv[/itex]1(modp)
    where in this case, a=18 and p=29


    3. The attempt at a solution
    By FLT, I found that 18[itex]^{28}[/itex][itex]\equiv[/itex]1(mod29)
    So, 18[itex]^{802}[/itex][itex]\equiv[/itex](18[itex]^{28}[/itex])[itex]^{28.5}[/itex]*18[itex]^{4}[/itex](mod29)[itex]\equiv[/itex]18[itex]^{4}[/itex](mod29)[itex]\equiv[/itex]25(mod29)

    So my solution is 25(mod29).
    However, the solution my professor posted is 4(mod29) (**NOT -4(mod29)**). Pretty confused here... Is there something wrong in my logic?
     
  2. jcsd
  3. Apr 4, 2012 #2

    tiny-tim

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    Science Advisor
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    hi bendaddy! :smile:
    isn't 1814 minus 1 ? :confused:
     
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