Question 82
A sequence $a_1, a_2, a_3, \ldots$ of positive integers is such that $a_{n+1}$ is the last digit of $a_n + a_{n-1}$ for all $n \gt 2$. Is it always true that for some $n_0$ the sequence $a_{n_0}, a_{n_0+1}, a_{n_0+2}, \ldots$ is periodic?