Midpoint criteria for solving Pell’s equation using the nearest square continued fraction

Matthews, KeithRobertson, JohnWhite, Jim2015-12-222015-12-220025-5718http://hdl.handle.net/1885/95164We derive midpoint criteria for solving Pell’s equation x2 −Dy2 = ±1, using the nearest square continued fraction expansion of √D. The period of the expansion is on average 70% that of the regular continued fraction.© 2009 American Mathematical SocietyKeywords: Nearest square continued fraction; Pell's equationMidpoint criteria for solving Pell’s equation using the nearest square continued fraction2010-0110.1090/S0025-5718-09-02286-82016-02-24