Prime linear recurrences are constant
Source: Philippines MO 2018/2
August 4, 2018
number theory
Problem Statement
Suppose is a sequence of integers, and is some integer. For all natural numbers ,
\begin{align*}\text{(i)} |a_n| \text{ is prime;} && \text{(ii)} a_{n+2} = a_{n+1} + a_n + d. \end{align*}
Show that the sequence is constant.