Pinko wrote: Let $n$ be a composite number and $a_1,a_2… a_k\in \mathbb{N}$ are the numbers smaller than $n$ and coprime with it (in this case $k=n-\phi (n)$). Let $b_1,b_2…b_k$ be a permutation of $a_1,a_2… a_k$ Prove that there exist indexes $i$ and $j$, $i\neq j$ for which $a_i b_i\equiv a_j b_j (mod $ $n)$. Shouldn't $k$ be $\phi(n)$ here

Pluto1708 wrote: Shouldn't $k$ be $\phi(n)$ here I made a mistake. It is "...and not coprime with it...".

Ooooooohhh, I WAS DOING THE WRONG PROBLEM FOR 3 HOURS