IMO Shortlist 2000 problem N1
Dodao/la:
arhiva2. travnja 2012. Determine all positive integers
![n\geq 2](/media/m/e/d/b/edbb3c15913fef4235c90cca2333a608.png)
that satisfy the following condition: for all
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
and
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
relatively prime to
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
we have
![a \equiv b \pmod n](/media/m/1/4/8/148af5f25801d7191206014af7c83778.png)
if and only if
![ab\equiv 1 \pmod n](/media/m/4/5/8/45888daf9acc722399e3fb2a38005d0f.png)
.
%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