MathDB
Sequence with divisibility

Source: Greek TST 2014-Pr.1.

June 23, 2014
inductionmodular arithmeticquadraticsnumber theory proposednumber theory

Problem Statement

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.
Back to ProblemsView on AoPS