There exists a number in this sequence that's divisible by $n$
Posted: Tue Mar 16, 2021 3:51 am
Let $a_0=0$, $a_1$ and $a_2$ are some integers. For all integer $k\geq3$, $a_k=5a_{k-1}+12a_{k-2}-13a_{k-3}$. Prove that for all positive integer $n$, there exists $m\leq n^3$ such that $n|a_m$.