MathNet 2026 — Part 05 Question 9

Let $(a_n)$ be the "iterated Fibonacci sequence": $a_n = f(f(n))$, where $f(1) = f(2) = 1$, and $f(n+2) = f(n+1) + f(n)$. Prove that $a_n$ is a multiple of 144 whenever it is a multiple of 14.