# Class numbers and divisiblity in the intersting cases

For n is belongs to the set of positive integers {2,3,4,...} => n > 1 and k belongs to {3, 7, 9, 11, 15, ...} => k also >1 but not 5 and 13. except 5 and 13 any odd number we can give to k. Now, is there any class numbers of Q(1 - 4$k^n$)^${1/2}$ are divisible by n? is there please justify?

Extension If we take n is even integer and grater than 5, then Q(1 - 4$k^n$)^${1/2}$ are divisible by n, other than for k = 13 and n = 8. Why this is happened? if we take less than 5 ( I mean for n = 2 or n = 4) what will happen?

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There's a link to a big table of class numbers at oeis.org/A000924 --- have you looked there for examples? –  Gerry Myerson Dec 13 '12 at 4:59