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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).

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    Append your work 'til now to the end of your question.2012-11-07

3 Answers 3