(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data.

1. Let [itex]a[/itex] and [itex]b[/itex] be constant integers with [itex]a \not = 0[/itex], and let the mapping [itex]f : Z \rightarrow Z[/itex] be defined by [itex]F(x) = ax + b[/itex]. Determine all values of [itex]a[/itex] such that f is a bijection. Prove that the aforementioned values are the only possible values resulting in a bijection.

The logic in my proof makes sense, but my conclusion that [tex] ax \cong 0 \mod a[/tex] doesn't make sense because that statement will always be true.

2. Relevant equations

N/A

3. The attempt at a solution

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# Mod. Arithmetic Proof: I don't see flaws in my logic, but it isn't working out.

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