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1976 IMO Problems/Problem 6

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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).

Solution

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See also

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