Hi everyone!
It's been a while since I posted anything. Today I'd like to talk about problem I from Oleksandr Kulkov Contest 2. Well, on some similar problem. Problem goes as follows: There is a rational number $$$x=\frac{p}{q}$$$, and you know that $$$1 \leq p, q \leq C$$$. You want to recover $$$p$$$ and $$$q$$$ but you only know number $$$r$$$ such that $$$r \equiv pq^{-1} \pmod{m}$$$ where $$$m > C^2$$$. In original problem $$$m$$$ was not fixed, instead you were allowed to query remainders $$$r_1,\dots,r_k$$$ of $$$x$$$ modulo several numbers $$$m_1,\dots,m_k$$$, which implied Chinese remainder theorem.