IMO 2006 Shortlist A1
A sequence of real numbers a0,a1,a2,... is defined by the formula ai+1 = baic · haii for i ≥ 0; here a0 is an arbitrary ...
Category: Algebra
Problem
A sequence of real numbers a0,a1,a2,... is defined by the formula ai+1 = baic · haii for i ≥ 0; here a0 is an arbitrary real number, baic denotes the greatest integer not exceeding ai, and haii = ai − baic. Prove that ai = ai+2 for i sufficiently large. (Estonia)