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Prove that terms of UK sequence are odd

Source: IMO ShortList 1988, Problem 28, United Kingdom 5, Problem 80 of ILL

November 9, 2005

inductionSequenceinequality systemIMO Shortlist

Problem Statement

The sequence

\{a_n\}

of integers is defined by a_1 \equal{} 2, a_2 \equal{} 7 and \minus{} \frac {1}{2} < a_{n \plus{} 1} \minus{} \frac {a^2_n}{a_{n \minus{} 1}} \leq \frac {}{}, n \geq 2. Prove that

a_n

is odd for all

n > 1.

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