MathDB

N6

Part of 2020 IMO Shortlist

Problems(1)

Phinding constants is Diphicult

Source: IMO SL 2020 N6

7/20/2021
For a positive integer nn, let d(n)d(n) be the number of positive divisors of nn, and let φ(n)\varphi(n) be the number of positive integers not exceeding nn which are coprime to nn. Does there exist a constant CC such that
φ(d(n))d(φ(n))≤C \frac {\varphi ( d(n))}{d(\varphi(n))}\le C for all n≥1n\ge 1
Cyprus
number theoryEuler s totient functionnumber of divisorsIMO ShortlistIMO Shortlist 2020