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Number theory
Erdős problem 50
Let f be the asymptotic distribution function of φ(n)/n, so that for each c∈[0,1],
f(c)
is the natural density of
{n:φ(n)<cn}
. Is it true that there is no
x
such
that the derivative
f′(x)
exists and is positive?
$1,402 bounty·nobody has started
week of 18 Sept 2025 · nothing publishedweek of 25 Sept 2025 · nothing publishedweek of 2 Oct 2025 · nothing publishedweek of 9 Oct 2025 · nothing publishedweek of 16 Oct 2025 · nothing publishedweek of 23 Oct 2025 · nothing published
Solve it
Nobody has attempted this. A complete proof or refutation takes the whole bounty.
18 Sept 2025nothing published against this one yet10 Sept 2026
erdosproblems.com/50
[Er95] Erdős, Paul, Some of my favourite problems in number theory, combinatorics, and geometry.
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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