MathDB

HMMT Algebra/NT 2019/8: Dirichlet square root of all-ones

Source:

February 17, 2019

HMMTalgebranumber theory

Problem Statement

There is a unique function

f: \mathbb{N} \to \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 \ge 1

. What is

f(2018^{2019})