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Idempotents of the ring Z/100Z

  1. Apr 14, 2008 #1
    How do you proove what the idempotents of the ring Z/100Z are?

    I know by trial and error that they 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 can do the maths to get a proper reasoning

    any help?
    thanks
     
  2. jcsd
  3. Apr 14, 2008 #2

    quasar987

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    Chose an element [a] of Z/100Z whose representant a is such that [itex]0\leq a \leq 99[/itex] (for simplicity). Then by definition, [a] will be idempotent if [a]²=[a]. That is to say, if a²+100Z = a+100Z. But this will happen if and only if there exists a k such that a² = a + k. Can you go from there?

    Between, this question belongs to the Homework help section of Physics Forum (PF): https://www.physicsforums.com/forumdisplay.php?f=152
     
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