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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 $\dfrac ab + \dfrac bc + \dfrac cd + \dfrac da.$

 
 Nov 21, 2020

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