Question 57
Let $a_{0}, a_{1}, a_{2}, \ldots$ be integers such that $a_{0}=19$, $a_{1}=25$, and for every $n \geq 0$ we have $a_{n+2}=2 a_{n+1}-a_{n}$. What is the smallest $i \gt 0$ for which $a_{i}$ is a multiple of $19$?
(A) 19
(B) 25
(C) 38
(D) 44
(E) 50
(A) 19
(B) 25
(C) 38
(D) 44
(E) 50