Determine all positive integers that satisfy the following condition: for all and relatively prime to we have if and only if .
%V0
Determine all positive integers $n\geq 2$ that satisfy the following condition: for all $a$ and $b$ relatively prime to $n$ we have $a \equiv b \pmod n$ if and only if $ab\equiv 1 \pmod n$.
Izvor: Međunarodna matematička olimpijada, shortlist 2000
Školjka 
that satisfy the following condition: for all 
and 
relatively prime to 
we have 
if and only if 
.