# Prove that if $[a] + [b] \equiv [a] + [c] \pmod n$, then $[b] \equiv [c] \pmod n$.

The question is very clear that we are dealing with classes. Does that change anything in this case? This was an unsolved example for class and I feel it's unusual that I don't know how to begin.

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How is the notation $[a]\equiv[b]\pmod n$ defined? Normally one would write either $a\equiv b\pmod n$ or $[a]=[b]$. Unless a definition of $[a]\equiv[b]\pmod n$ has been given, I’d regard the notation in the title as at an error on the part of the person who wrote up the question.