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Proof of zero divisor existence.

  1. Feb 22, 2013 #1
    1. Let a != 0 and b be elements of the integers mod n. If the equation ax=b has no solution in Zn then a is a zero divisor in Zn



    3. The attempt at a solution

    Not sure where to start on this proof, I keep trying to find something using the properties of modular arithmetic but am coming up empty
     
  2. jcsd
  3. Feb 22, 2013 #2

    jbunniii

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    Hint: If ##ax = b## has no solutions, then that means the map ##\phi : Z_n \rightarrow Z_n## defined by ##\phi(x) = ax## is not surjective. Since ##Z_n## is finite, what else does that imply about ##\phi##?
     
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