grandes-ecoles 2022 Q7.2

grandes-ecoles · France · x-ens-maths-d__mp Number Theory GCD, LCM, and Coprimality

Let $n$ be an integer coprime to $d$. Show that the map $$(a,b)\mapsto(na,nb)$$ is a bijection from $S_{\mathrm{prim}}(d)$ to $S_{\mathrm{prim}}(d)$.

Let $n$ be an integer coprime to $d$. Show that the map
$$(a,b)\mapsto(na,nb)$$
is a bijection from $S_{\mathrm{prim}}(d)$ to $S_{\mathrm{prim}}(d)$.