Question 181
Let $a$, $b$, $c$ be given positive integers. Prove there exists some positive integer $N$ such that
$$
\begin{aligned}
a &\mid Nbc + b + c \\
b &\mid Nca + c + a
\end{aligned}
$$
$$
\begin{aligned}
a &\mid Nbc + b + c \\
b &\mid Nca + c + a
\end{aligned}
$$