Question

Find all integers $\sf{n \geq 3}$ for which there exists real numbers $\sf{a_1, a_2, \dots, {a}_{n+2}}$ such that $\sf{{a}_{n+1} = a_1}$, and $\sf{{a}_{n+2} = a_2}$, and
$\sf{ {a}_{i}{a}_{i+1} + 1 = {a}_{i+2} }$
for $\sf{i = 1, 2, \dots, n}$​

Answer 1

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