Hungary-Israel Binational 2008\5
Source: recursive sequence, prove that the terms are integers
November 5, 2008
inductionalgebra proposedalgebra
Problem Statement
The sequence is defined as follows: a_0\equal{}1, a_1\equal{}1, a_{n\plus{}1}\equal{}\frac{1\plus{}a_{n}^2}{a_{n\minus{}1}}.
Prove that all the terms of the sequence are integers.