BG-MO 1978 Problem 1

We are given the sequence $a_1,a_2,a_3,\ldots$ , for which: $$a_n=\frac{a^2_{n-1}+c}{a_{n-2}}\enspace\text{for all }n>2.$$ Prove that the numbers $a_1$ , $a_2$ and $\frac{a_1^2+a_2^2+c}{a_1a_2}$ are whole numbers.