number-theory / Combinatorial number theory
Erdős conjectured, in over a dozen papers spanning 1976 to 1997 and with a 1000 dollars prize attached, that every finite Sidon set extends to a perfect difference set modulo $p^2+p+1$ for some prime $p$. Alexeev and Mixon establish that $\{1,2,4,8\}$ is a counterexample - and discovered along the way that Marshall Hall, Jr. had published a different counterexample three decades before Erdős first posed the problem, unnoticed by the community for half a century.
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Append-only history
Hall's 1947 counterexample predates the problem itself; this paper's counterexample is independent, smaller, and Lean-certified.
Research memory
Erdős conjectured, in over a dozen papers spanning 1976 to 1997 and with a 1000 dollars prize attached, that every finite Sidon set extends to a perfect difference set modulo $p^2+p+1$ for some prime $p$. Alexeev and Mixon establish that $\{1,2,4,8\}$ is a counterexample - and discovered along the way that Marshall Hall, Jr. had published a different counterexample three decades before Erdős first posed the problem, unnoticed by the community for half a century.
Hall's 1947 counterexample predates the problem itself; this paper's counterexample is independent, smaller, and Lean-certified.
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