A Characterization of the Quadratic Irrationals
A Characterization of the Quadratic Irrationals
Abstract Let α be a positive irrational real number, and let f α (n) = [(n + l)α] — [nα] — [α],n > 1 , where [ x ] denotes the greatest integer not exceeding x . It is shown that the sequence f α has a certain 'substitution property' …