Turkey TST 2008 Q4
Source:
April 2, 2008
inductionnumber theory unsolvednumber theory
Problem Statement
The sequence is defined as; x_1\equal{}a, x_2\equal{}b and for all positive integer , x_{n\plus{}2}\equal{}2008x_{n\plus{}1}\minus{}x_n. Prove that there are some positive integers such that 1\plus{}2006x_{n\plus{}1}x_n is a perfect square for all positive integer .