Question 78
Let $k$ be a rational number greater than $1$ (correction by Fengning Ding). Prove that there exist positive integers $a, b, c$ satisfying the equations
$$
\begin{aligned}
a^{2}+b^{2} & =c^{2} \\
\frac{a+c}{b} & =k .
\end{aligned}
$$
$$
\begin{aligned}
a^{2}+b^{2} & =c^{2} \\
\frac{a+c}{b} & =k .
\end{aligned}
$$