1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper

    hi bendaddy! :smile:
    isn't 1814 minus 1 ? :confused:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook