# Set problem. Need it well written...

We have $k,m \in \N^*$. Define two sets U and V by:

U = {$a \in \Z | 1 \leq a \leq m, gcd(a,m) = 1$}
V = {$a \in \Z | 1 \leq a \leq km, gcd(a,km) = k$}

a. We have $a \in U$. Show that $ka \in V$
b. Thanks to (a.) we can define a function $f: U \to V$ by $a \to ka$. Show that f is a bijection.
You can use, without proof, the solution: for $k,x,y \in \Z, gcd(kx,ky) = |k|gcd(x,y)$