MathNet 2017-part-03 — 176 problems (EN–VI) Question 174

Let $\left(a_{n}\right)_{n=1}^{\infty}$ be a sequence of integers satisfying the relation $a_{n+1}=a_{n}^{1009}+3^{2017}$, $\forall n \geq 1$. How many perfect squares can this sequence contain? Justify your answer.