PPL 058 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.26
Prize Problem LedgerErdősPPL 058Erdős Problem #50

Permanent problem IDPPL 058

Verified openErdősconjecture

Number theory

Erdős Problem #50

Schoenberg proved that for every c∈ [0,1] the density of { n∈ ℕ : φ(n)<cn} exists. Let this density be denoted by f(c). Is it true that there are no x such that f'(x) exists and is positive?

number theory
01

The problem

Schoenberg proved that for every c∈ [0,1] the density of { n∈ ℕ : φ(n)<cn} exists. Let this density be denoted by f(c). Is it true that there are no x such that f'(x) exists and is positive?

Open since1995exact
Last checked2026.07.26Catalog verification
02

Reward offers

Offer 01$250Paul Erdős / Combinatorics Foundation
Documented

A solution must appear in a reputable journal, with documentation that Erdős offered the displayed amount. Claims are administered by the Combinatorics Foundation; erdosproblems.com does not pay awards.

03

Sources & reading