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OSP SMA 2006 Bagian Kedua No 5

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Misalkan $a$, $b$, $c$ bilangan-bilangan asli. Jika semua akar ketiga persamaan

\begin{eqnarray*}

x^2+ax+b &=& 0 \\

x^2+bx+c &=& 0 \\

x^2+cx+a &=& 0

\end{eqnarray*}

adalah bilangan asli, tentukan $a$, $b$, dan $c$.

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