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### How to prove that $f(x)=x^3 \pmod{pq}$ is bijective for any non negative integer $x<pq$ where 3 is not a factor of $p-1$ and $q-1$?

Well you might begin by observing that if $x^3\equiv y^3$ then $x^3-y^3=(x-y)(x^2+xy+y^2)\equiv 0$ Then $pq$ cannot be a factor of $x-y$ because $x$ and $y$ are too small by hypothesis. So this means ...
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