Consider the Somos 3 sequence $a_{n+3}a_n = a_{n+1}a_{n+2}$ with $a_1 = \alpha$, $a_2 = \beta$ and $a_3 = \gamma$ where $\alpha$, $\beta$ and $\gamma$ are all integers.
(a) Try different values of the initial data to see whether it generates integer sequences.
(b) From your observation, formulate the conditions on $\alpha$, $\beta$ and $\gamma$ which guarantee that the sequences generated are integers.
(c) Prove your statement formulated in (b).