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2018 IMO Problems/Problem 2

Revision as of 22:34, 9 July 2018 by Moaaz (talk | contribs) (Created page with "Find all numbers <math>n \ge 3</math> for which there exists real numbers <math>a_1, a_2, ..., a_{n+2}</math> satisfying <math>a_{n+1} = a_1, a_{n+2} = a_2</math> and <cmath>...")
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Find all numbers $n \ge 3$ for which there exists real numbers $a_1, a_2, ..., a_{n+2}$ satisfying $a_{n+1} = a_1, a_{n+2} = a_2$ and \[a_{i}a_{i+1} + 1 = a_{i+2}\] for $i = 1, 2, ..., n.$

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