MathDB
NT recurrence, condition for 7|x_n

Source: Yugoslav TST 1987 P1

May 28, 2021
recurrence relationnumber theorySequences

Problem Statement

Let x0=a,x1=bx_0=a,x_1=b and xn+1=2xn−9xn−1x_{n+1}=2x_n-9x_{n-1} for each n∈Nn\in\mathbb N, where a,ba,b are integers. Find the necessary and sufficient condition on aa and bb for the existence of an xnx_n which is a multiple of 77.
Back to ProblemsView on AoPS