Erdős-Straus ConjectureACTIVE
4/n = 1/x + 1/y + 1/z
For every integer n ≥ 2, there exist positive integers x, y, z such that 4/n = 1/x + 1/y + 1/z
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Collatz ConjectureACTIVE
n → n/2 or 3n+1
For any positive integer, repeatedly applying n→n/2 (if even) or n→3n+1 (if odd) eventually reaches 1.
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Sidon Sets ExtensionDISPROVED
{1,2,4,8,13} counterexample
A Sidon set has all pairwise sums distinct. The set {1,2,4,8,13} cannot extend to a perfect difference set.
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