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Homework Help: Cryptology and Congruence

  1. Oct 17, 2009 #1
    1. The problem statement, all variables and given/known data
    Let n be a positive integer. Consider the congruence equation 59x + 15 congruent to 6 mod n
    For this equation, a solution x exits. Why?

    2. Relevant equations

    3. The attempt at a solution
    there is a k such that
    (59x +15) - 6 = kn
    (59x +15) - kn = 6
    59x - kn = 6 - 15
    59x - kn = -9
    there is a linear combination of 59 and k that gives -9
    But then, I don't know if this is the right way to go and what to do now!
    Thanks to help
  2. jcsd
  3. Oct 17, 2009 #2


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    Science Advisor
    Homework Helper

    If n=59 there is no solution. You have to know something about n to decide whether there is a solution.
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