Let h(n) be maximal such that if A⊆Z with ∣A∣=n
then there is B⊆A with ∣B∣≥h(n) such that if
a1+⋯+ar=b1+⋯+bs with ai,bi∈B then r=s.
Is h(n)=Θ(n)?
$4,969 bounty·nobody has started
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17 Oct 2025nothing published against this one yet9 Oct 2026
Solve it
Nobody has attempted this. A complete proof or refutation takes the whole bounty.
[Str66] Straus, E. G., On a problem in combinatorial number theory. J. Math. Sci. (1966), 77--80.
[Er62c] Erdős, Pál, Some remarks on number theory. {III}. Mat. Lapok (1962), 28--38.
[Ch74b] Choi, S. L. G., On an extremal problem in number theory. J. Number Theory (1974), 105--111.
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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