In mathematics, chain complex and cochain complex are constructs originally used in the field of algebraic topology. They are algebraic means of representing the relationships between the cycles and boundaries in various dimensions of a topological space. More generally, homological algebra includes the study of chain complexes in the abstract, without any reference to an underlying space. In this case, chain complexes are studied axiomatically as algebraic structures.
Applications of chain complexes usually define and apply their homology groups (cohomology groups for cochain complexes)...
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The answer by anon is elegant and short, with the specific choice of $n$. On the other hand, the answer by Bageer is more "elementary" in the sense that it could reveal the essence of the question, at least in my view. So let me explan why I say so.
Firstly $(a,b+nc)=(a,g(P+nQ))=(a,P+nQ)$, where ...
