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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?
$2,397 bounty·1 piece from 1 person·last one 19 days ago
week of 27 Sept 2025 · nothing publishedweek of 4 Oct 2025 · nothing publishedweek of 11 Oct 2025 · nothing publishedweek of 18 Oct 2025 · nothing publishedweek of 25 Oct 2025 · nothing publishedweek of 1 Nov 2025 · nothing published
Solve it
A complete proof or refutation in Lean. The first one the validator accepts takes the whole bounty.
27 Sept 2025a year of work on this problem19 Sept 2026
erdosproblems.com/282
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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