two sequences
Source: Vietnam NMO 1987 Problem 2
February 4, 2009
algorithmalgebrapolynomialmodular arithmeticalgebra unsolved
Problem Statement
Sequences and are constructed as follows: x_0 \equal{} 365, x_{n\plus{}1} \equal{} x_n\left(x^{1986} \plus{} 1\right) \plus{} 1622, and y_0 \equal{} 16, y_{n\plus{}1} \equal{} y_n\left(y^3 \plus{} 1\right) \minus{} 1952, for all . Prove that \left|x_n\minus{} y_k\right|\neq 0 for any positive integers , .