1976 IMO Problems/Problem 6

Problem

A sequence $(u_{n})$ is defined by

$u_{0} = 2 \quad u_{1} = \frac {5}{2}, u_{n + 1} = u_{n}(u_{n - 1}^{2} - 2) - u_{1} \quad \textnormal{for} n = 1,\ldots$

Prove that for any positive integer $n$ we have

$\lfloor u_{n} \rfloor = 2^{\frac {(2^{n} - ( - 1)^{n})}{3}}$

(where $\lfloor x\rfloor$ denotes the smallest integer $\leq$ $x$ ) $.$

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1976 IMO (Problems) • Resources
Preceded by Problem 5	1 • 2 • 3 • 4 • 5 • 6	Followed by Final Question
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