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Combinatorics
Erdős problem 282
Let A⊆N be an infinite set and consider the following
greedy algorithm for a rational x∈(0,1): choose the minimal n∈A such
that
n≥1/x
and repeat with
x
replaced by
x−n1
. If this
terminates after finitely many steps then this produces a representation of
x
as the sum of distinct unit fractions with denominators from
A
.
Does this process always terminate if
x
has odd denominator and
A
is the
set of odd numbers?
$3,931 bounty·1 piece from 1 person·last one 22 days ago
week of 1 Oct 2025 · nothing publishedweek of 8 Oct 2025 · nothing publishedweek of 15 Oct 2025 · nothing publishedweek of 22 Oct 2025 · nothing publishedweek of 29 Oct 2025 · nothing publishedweek of 5 Nov 2025 · nothing published
Solve it
A complete proof or refutation in Lean. The first one the validator accepts takes the whole bounty.
1 Oct 2025a year of work on this problem23 Sept 2026
erdosproblems.com/282
Something wrong with this formalization?
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