2020? But it's still 2015!
Algebra
Level
5
\[\large f(x+1) = (5^{2^{x-1}} + 1)(x+1)^{2}f(x)\]
Suppose we define a function of \(x\) as described above for \(x\) is a non-negative integer with \(f(0)=\sqrt{5} - 1\).
If the value of \(f(2020)\) can be written in form \((5^{p} - 1)(q!)^{2}\), for positive integers \(p\) and \(q\), find \(\frac{2^{q}}{p}\).
by
Muhammad Rizki Fadillah