A Characterization of the Quadratic Irrationals

Canadian Mathematical Bulletin - Tập 34 Số 1 - Trang 36-41 - 1991
Tom C. Brown1
1Department of Mathematics and Statistics Simon Fraser University Burnaby, BC V5A ISA

Tóm tắt

AbstractLet 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.

Từ khóa


Tài liệu tham khảo

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Thông tin
Thông tin xuất bản

Canadian Mathematical Bulletin

Tập 34 Số 1

36-41

Thông tin tác giả