Question 43
Let $(x_n)$, $n \ge 1$, be a sequence of real numbers with $x_1 = 1$, such that $2x_{n+1} = 3x_n + \sqrt{5x_n^2 - 4}$, for $n=1,2,3,...$
a. Prove that all terms of the sequence are natural numbers.
β. Examine if there exist a term of the sequence divisible by $2011$.
a. Prove that all terms of the sequence are natural numbers.
β. Examine if there exist a term of the sequence divisible by $2011$.