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For every $k \in {\mathbb Z}$ construct a continuous map $f: S^n \to S^n$ with $\deg(f) = k$.
How do I show that for any $n>0$ and any $m$ any integer, there exists a map $f: S^n\to S^n$ of degree $m$?
I am trying a constructive proof(constructing such a map) but I still did not find a map whose degree is not $1$ or $-1$. I am viewing this question from a singular homology point of view.
Thanks.