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Divisibility in arithmetic

  1. Apr 25, 2012 #1
    Chinese remainder theorem help

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

    Solve in [tex]Z^{2}:6x-5y=1[/tex]

    Conclude the solution to the system:

    X≡2(mod5) , X≡1(mod6)

    3. The attempt at a solution

    1- solved the equation and found one unique solution which was S={(1,1)}

    X≡2(mod5) , X≡1(mod6)

    X≡2(mod5) means X=5t+2

    X≡1(mod6) means 5t+2=1(mod6) which is 5t=-1(mod6) But how can i proceed from here on?
    Last edited: Apr 25, 2012
  2. jcsd
  3. Apr 25, 2012 #2
    Solved it :)
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