MathDB
fractional recurrence, output is integer

Source: Yugoslav TST 1980 P3

May 29, 2021
number theorySequencesrecurrence relation

Problem Statement

A sequence (xn)(x_n) satisfies xn+1=xn2+axn−1x_{n+1}=\frac{x_n^2+a}{x_{n-1}} for all n∈Nn\in\mathbb N. Prove that if x0,x1x_0,x_1, and x02+x12+ax0x1\frac{x_0^2+x_1^2+a}{x_0x_1} are integers, then all the terms of sequence (xn)(x_n) are integers.
Back to ProblemsView on AoPS