HMMT 2019 A8

There is a unique function $f: \mathbb{N} \rightarrow \mathbb{R}$ such that $f(1)>0$ and such that

$\sum_{d \mid n} f(d) f\left(\frac{n}{d}\right)=1$

for all $n \geq 1$ . What is $f\left(2018^{2019}\right)$ ?

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

\frac{\binom{4038}{2019}^{2}}{2^{8076}}

Solutions

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