Let \(a_0,a_1,\cdots\) be a sequence defined by \(a_0=7\), \(a_1=8\), and, for all \(n\ge 2\), \[a_n=5a_{n-1}-6a_{n-2}\] Find the remainder when \(a_{2014}\) is divided by 1000.
See here for information regarding recurrence relations.
by
Daniel Chiu
