I encountered this problem when I was doing a course in Duolingo. It marked me wrong to write
We haven't bought such thing.
The correct one according to Duolingo is:
We haven't bought such a thing.
I read the comment section. There was a native American commented that it's wrong to write . He/she also added that a native speaker would likely to say either:
We have bought no such thing.
We haven't bought such things.
Since it's a standalone sentence, I don't know what thing refers to. Supposing the thing is a bottle of wine, does that mean I could say  or ? Also, if it's two bottles should I use ? In addition to that, what if it's an uncountable noun like furniture? Why do  and  make a difference?