Geodesic
Cyclic subgroups of ideal class groups in real quadratic orders
Glasgow mathematical journal, Tome 41 (1999) no. 2, pp. 197-206

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The primary purpose of this paper is to provide general sufficient conditions for any real quadratic order to have a cyclic subgroup of order n∈N in its ideal class group. This generalizes results in the literature, including some seminal classical works. This is done with a simpler approach via the interplay between the maximal order and the non-maximal orders, using the underlying infrastructure via the continued fraction algorithm. Numerous examples and a concluding criterion for non-trivial class numbers are also provided. The latter links class number one criteria with new prime-producing quadratic polynomials. 
Mollin, R. A. Cyclic subgroups of ideal class groups in real quadratic orders. Glasgow mathematical journal, Tome 41 (1999) no. 2, pp. 197-206. doi: 10.1017/S0017089599970799
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     title = {Cyclic subgroups of ideal class groups in real quadratic orders},
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     year = {1999},
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     doi = {10.1017/S0017089599970799},
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