A sequence $(a_n)$ positive integers is determined by equalities $a_1=20,a_2=22$ and $a_{n+1}=4a_n^2+5a_{n-1}^3$ for all $n \geq 2$. Find the maximum power of two which divides $a_{2023}$.
Source: Belarusian National Olympaid 2023
Tags: number theory
A sequence $(a_n)$ positive integers is determined by equalities $a_1=20,a_2=22$ and $a_{n+1}=4a_n^2+5a_{n-1}^3$ for all $n \geq 2$. Find the maximum power of two which divides $a_{2023}$.