MathDB

6.1

Part of MathLinks Contest 7th

Problems(1)

0761

Source:

6/23/2008
Let {xn}n≥1 \{x_n\}_{n\geq 1} be a sequences, given by x_1 \equal{} 1, x_2 \equal{} 2 and x_{n \plus{} 2} \equal{} \frac { x_{n \plus{} 1}^2 \plus{} 3 }{x_n} . Prove that x2008 x_{2008} is the sum of two perfect squares.
inductionstrong induction