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!

Number Theory - Largest Impossible Score

  1. Feb 25, 2007 #1
    Edit: I finally figured this problem out, although I didn't use residue systems, so a solution is no longer necessary.

    1. The problem statement, all variables and given/known data

    For this problem, I need to find a fomula for the largest unattainable score in a game where you can either score m or n points at a time (m and n are relatively prime) and prove that this formula will always work. Complete residue systems are suggested to be used in the proof.

    2. Relevant equations

    {0, n, 2n, 3n, ... , (m-1)n} is a complete residue system mod m when m and n are relatively prime.

    3. The attempt at a solution

    Through trial and error, I have found that the largest impossible score is mn - (m+n). I'm stuck, however, on proving this. I don't even know how to start, so any help would be greatly appreciated.
    Last edited: Feb 25, 2007
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted