Let $a$, $b$, $c$, and $d$ be positive integers. We know that
\(\begin{align*} a+b&=kc,\\ b+c&=kd,\\ c+d&=ka,\\ d+a&=kb. \end{align*}\)
Find the maximum of $\dfrac ab + \dfrac bc + \dfrac cd + \dfrac da.$
I'm getting a maximum value of 5.
