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Number theory
Date added
Erdős problem 291 - part i
Let n≥1 and define Ln to be the least common multiple of {1,…,n}
and
an
by
∑1≤k≤nk1=Lnan
.
Is it true that
(an,Ln)=1
occurs for infinitely many
n
?
$2,439 bounty·1 piece from 1 person·last one 10 days ago
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
A complete proof or refutation in Lean. The first one the validator accepts takes the whole bounty.
18 Sept 2025a year of work on this problem10 Sept 2026
erdosproblems.com/291
[ErGr80, p.34] Erdős, P. and Graham, R., Old and new problems and results in combinatorial number theory. Monographies de L'Enseignement Mathematique (1980).
[Sh16] P. Shiu, The denominators of harmonic numbers. arXiv:1607.02863 (2016).
[WuYa22] Wu, Bing-Ling and Yan, Xiao-Hui, On the denominators of harmonic numbers. {IV}. C. R. Math. Acad. Sci. Paris (2022), 53--57.
Something wrong with this formalization?
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