Hungary-Israel Binational 1999\4
Source: Prove that a sequence containts only integers
October 30, 2008
inequalitiesalgebrapolynomialalgebra proposed
Problem Statement
is a positive integer. Consider the following recursive sequence: a_1\equal{}c, a_{n\plus{}1}\equal{}ca_{n}\plus{}\sqrt{(c^2\minus{}1)(a_n^2\minus{}1)}, for all .
Prove that all the terms of the sequence are positive integers.