Discrete Math - Modular Arithmetic

  1. 1. The problem statement, all variables and given/known data
    For which values of n≥2 does the implication:

    axb=0 ⇔ a=0 or b=0

    For some Zn (n should be a subscript)

    NOTE: For the a x b, the x should be the x that has a circle around it. I didn't see that symbol in the "quick symbols" :)

    2. Relevant equations
    I know that this is true when n is a prime (answer in back of book), but I don't understand why. For example, if a=5 and b = 4, then that would also be 0 for n=5, right? Do I just not understand how to do modular arithmetic?

    Thanks!
     
  2. jcsd
  3. HallsofIvy

    HallsofIvy 40,689
    Staff Emeritus
    Science Advisor

    What is your definition of that symbol? I would have interpreted as a "tensor product" but that doesn't really make sense here. I suspect it is a "special operation" your text is defining for this problem.
     
  4. tiny-tim

    tiny-tim 26,043
    Science Advisor
    Homework Helper

    hi hammonjj! :smile:
    ah, but 5 = 0 :wink:
     
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