Period-length equality for the nearest integer and nearest square continued fraction expansions of a quadratic surd

Matthews, KeithRobertson, John2015-12-070017-095Xhttp://hdl.handle.net/1885/19488We prove equality of the period-lengths of the nearest integer continued fraction and the nearest square continued fraction, for arbitrary real quadratic irrationals.Keywords: Nearest integer continued fraction; Nearest square continued fraction; Period-length; Reduced quadratic irrationalPeriod-length equality for the nearest integer and nearest square continued fraction expansions of a quadratic surd201110.3336/gm.46.2.012016-02-24