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Part of 2014 Greece Team Selection Test

Problems(1)

Sequence with divisibility

Source: Greek TST 2014-Pr.1.

6/23/2014
Let (xn) n≥1(x_{n}) \ n\geq 1 be a sequence of real numbers with x1=1x_{1}=1 satisfying 2xn+1=3xn+5xn2−42x_{n+1}=3x_{n}+\sqrt{5x_{n}^{2}-4}
a) Prove that the sequence consists only of natural numbers. b) Check if there are terms of the sequence divisible by 20112011.
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