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Generalized continued fractions in real quadratic fields and Pell’s equations. (English)
JP J. Algebra Number Theory Appl. 22, No. 2, 211-223 (2011).
This is the result of a successful research experience for undergraduates (REU) project. The main result is the determination of the Rosen $λ$-fraction [{\it D. Rosen}, Duke Math. J. 21, 549‒563 (1954; Zbl 0056.30703)] expansion of all units of the ring of integers of $\mathbb Q(λ)$ when $λ= \sqrt{d}$ with $d>0$ square-free, thus generalizing a result of {\it D. Rosen} and {\it C. Towse} [ Arch. Math. 77, No. 4, 294‒302 (2001; Zbl 0992.11034)].
Reviewer: Thomas Schmidt (Corvallis)
Classification: F65