The sequence (xn) is defined as; x_1\equal{}a, x_2\equal{}b and for all positive integer n, x_{n\plus{}2}\equal{}2008x_{n\plus{}1}\minus{}x_n. Prove that there are some positive integers a,b such that 1\plus{}2006x_{n\plus{}1}x_n is a perfect square for all positive integer n. inductionnumber theory unsolvednumber theory