Is pi^pi^pi^pi an integer?
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3%
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Resolves once a proof is published.
Some background: https://www.youtube.com/watch?v=BdHFLfv-ThQ
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WolframAlpha seems to be under the impression that it knows the answer, but I suspect it is mistaken.
https://www.wolframalpha.com/input?i=Is+pi%5Epi%5Epi%5Epi+an+integer%3F