MathDB
Rational sequence

Source: Polish MO Second round 2024 P1

February 9, 2024
algebra

Problem Statement

Does there exist a rational x1x_1, such that all members of the sequence x1,x2,…,x2024x_1, x_2, \ldots, x_{2024} defined by xn+1=xn+xn2−1x_{n+1}=x_n+\sqrt{x_n^2-1} for n=1,2,…,2023n=1, 2, \ldots, 2023 are greater than 11 and rational?
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