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Shaun
Shaun
3:09 PM
The following answer of mine got a downvote and I don't know why
4
A: Suppose $[a],[b],[c]\in\Bbb Z_n$, and are residue classes which satisfy $[a][b]=[1]$ and $[a][c]=[1]$. Prove $[b]=[c]$.

ShaunWe have $$\begin{align} [b]&=[b1]\\ &=[b]\color{red}{[1]}\\ &=[b](\color{red}{[a][c]})\\ &=([b][a])[c]\\ &=[ba][c]\\ &=[ab][c]\\ &=(\color{blue}{[a][b]})[c]\\ &=\color{blue}{[1]}[c]\\ &=[1c]\\ &=[c]. \end{align}$$

 

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