MathDB
a_{n+2 }= 15a_{n+1} + 16a_n, infinite integers k such that 269 \ a_k

Source: Norwegian Mathematical Olympiad 2017 - Abel Competition p2

September 3, 2019
Sequencenumber theorydivides

Problem Statement

Let the sequence an be defined by a0=2,a1=15a_0 = 2, a_1 = 15, and an+2=15an+1+16ana_{n+2 }= 15a_{n+1} + 16a_n for n≥0n \ge 0. Show that there are infinitely many integers kk such that 269∣ak269 | a_k.
Back to ProblemsView on AoPS