Lower bounds for the class number and the caliber of certain real quadratic fields (Q1913560)

We quote the author's words: ``We give some canonical cycles of reduced ideals for the real quadratic fields \(K= \mathbb Q(\sqrt {m})\) with \(m= 4q^2+1\), \(m= q^2+4\) (\(q\) odd), \(m= q^2 +1\) (\(q\) odd) and \(m= q^2\pm 2\) (\(q\) odd). Lower bounds of the class number \(h(K)\) and the caliber \(\mathrm{Cal}(K)\) (number of reduced ideals) are given. Some of those lower bounds for the class number are obtained, by other methods in [\textit{R. A. Mollin}, Proc. Japan Acad., Ser. A 66, 109--111 (1990; Zbl 0714.11068)]''.