herbert granzow on Sat, 23 Aug 2008 16:26:36 +0200

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class number of IQ(2^{1/n})

Are there statements about the class number of IQ(2^{1/n}) (beside general
theorems like the Minkowski bound)?

Using PARI, I found that it equals 1 for n <= 46.

Does someone know a n for which the class number is > 1?

It can't be known that it is always 1 since this would solve an open