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Cohn asks if for every real quadratic field Q(m) with discriminant d thereexists a non-maximal order corresponding to f > 1 such that the relative classnumber Hd(f) = h(f2d)/h(d) is one. We prove that when m = 46 (and in sevenother cases) there is no such order.

Real Quadratic Fields In Which Every Non-Maximal Order Has Relative Class Number Greater Than One