Question 6
Let $f: \mathbb{Z}_{\geq 0} \rightarrow \mathbb{Z}_{\geq 0}$ be a function which satisfies for all integer $n \geq 0$ :
(a) $f(2n+1)^2 - f(2n)^2 = 6f(n) + 1$,
(b) $f(2n) \geq f(n)$;
where $\mathbb{Z}_{\geq 0}$ is the set of nonnegative integers. Solve the equation $f(n) = 1000$.
(a) $f(2n+1)^2 - f(2n)^2 = 6f(n) + 1$,
(b) $f(2n) \geq f(n)$;
where $\mathbb{Z}_{\geq 0}$ is the set of nonnegative integers. Solve the equation $f(n) = 1000$.