On the sum of a prime and two Fibonacci numbers

Ji-Zhen Xu, Yong-Gao Chen

Let $\{f_n\}$ be the Fibonacci sequence. For any positive integer $n$, let $r(n)$ be the number of solutions of $n=p+f_{k_1^2}+f_{k_2^2}$, where $p$ is a prime and $k_1, k_2…