A Characterization of the Quadratic Irrationals
- 1 March 1991
- journal article
- Published by Canadian Mathematical Society in Canadian Mathematical Bulletin
- Vol. 34 (1) , 36-41
- https://doi.org/10.4153/cmb-1991-006-4
Abstract
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.Keywords
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