For every n, the Brauer-Manin obstruction does not obstruct positive integer solutions to the Erdos-Straus equation, yet it gives a universal local condition (a product of Hilbert symbols equal to -1) for all such solutions.
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Brauer-Manin obstruction for Erd\H{o}s-Straus surfaces
For every n, the Brauer-Manin obstruction does not obstruct positive integer solutions to the Erdos-Straus equation, yet it gives a universal local condition (a product of Hilbert symbols equal to -1) for all such solutions.