Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Idempotents of Z/100Z

  1. Apr 14, 2008 #1
    1. The problem statement, all variables and given/known data
    How do you proove what the idempotents of the commutative ring Z/100Z are?

    2. Relevant equations

    elements 'a' are idempotent if a^2 = a i.e a(a-1)=0
    Find the integers 0 < a < 99 (inclusive), such that 100 divides a(a-1)

    3. The attempt at a solution

    I know by trial and error that the answers are the elements 0,1,25,76 but have no proof as to why this is.
    i know i have to find the integers 'a' such that 100 divides a(a-1)=a^2 -a but cant do the maths to get a proper reasoning

    100 = 2x2x5x5, so does that mean if 100 divides a(a-1) that 2 divides a(a-1) as would 5.
    the problem is this wouldnt lead me to any of the known solutions either?

    Thanks for any help
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

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