IMO Shortlist 1988 problem 28
Dodao/la:
arhiva2. travnja 2012. The sequence
![\{a_n\}](/media/m/2/5/2/252d82e82000c8ff418959c98eeed9e9.png)
of integers is defined by
and
Prove that
![a_n](/media/m/1/f/f/1ff6f81c68b9c6fb726845c9ce762d7a.png)
is odd for all
%V0
The sequence $\{a_n\}$ of integers is defined by
$$a_1 = 2, a_2 = 7$$
and
$$- \frac {1}{2} < a_{n + 1} - \frac {a^2_n}{a_{n - 1}} \leq \frac {}{}, n \geq 2.$$
Prove that $a_n$ is odd for all $n > 1.$
Izvor: Međunarodna matematička olimpijada, shortlist 1988