# 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.

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Thank you, there was no definition, just my confusion. –  grayQuant Feb 15 '13 at 0:58
@grayQuant: That’s what I was afraid of. In that case I’d treat it as if it were written without the square brackets. If it’s something that’s to be handed in, I’d explain why I was doing so. –  Brian M. Scott Feb 15 '13 at 0:59
Ethan I do write in Tex, there was no need. –  grayQuant Feb 15 '13 at 1:01
@grayQuant My bad, sorry. –  Ethan Feb 15 '13 at 1:02
I should have done a better job explaining, my confusion is why [] were used, I assumed classes. The problem was presented to me in that way without further explanation. @BrianM.Scott – grayQuant just now edit –  grayQuant Feb 15 '13 at 1:04