Geodesic
A Characterization of the Quadratic Irrationals
Canadian mathematical bulletin, Tome 34 (1991) no. 1, pp. 36-41

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Let α be a positive irrational real number, and let fα (n) = [(n + l)α] — [nα] — [α],n > 1, where [x] denotes the greatest integer not exceeding x. It is shown that the sequence fα has a certain 'substitution property' if and only if α is the root of a quadratic equation over the rationals.
DOI : 10.4153/CMB-1991-006-4
Mots-clés : 10L10 
Brown, Tom C. A Characterization of the Quadratic Irrationals. Canadian mathematical bulletin, Tome 34 (1991) no. 1, pp. 36-41. doi: 10.4153/CMB-1991-006-4
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     title = {A {Characterization} of the {Quadratic} {Irrationals}},
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     year = {1991},
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