MathNet 2004 — Part 01 Question 99

Consider the sequence $(a_n)_{n \in \mathbb{N}}$ with $a_0 = a_1 = a_2 = a_3 = 1$ and $a_n a_{n-4} = a_{n-1} a_{n-3} + a_{n-2}^2$, $n \ge 4$. Prove that all the terms of this sequence are integer numbers.