Problem A. 395. (March 2006)
A. 395. Let 1<a<2 be a real number. (a) Show that there exists a unique sequence x1,x2,... of positive integers satisfying xi+1xi2 for all indices i and
(b) Prove that inequality xi+1>xi2 holds for infinitely many indices if and only if a is irrational.
Deadline expired on April 18, 2006.
11 students sent a solution. 5 points: Hujter Bálint, Kisfaludi-Bak Sándor, Nagy 224 Csaba, Paulin Roland. 4 points: Erdélyi Márton, Tomon István. 3 points: 1 student. 2 points: 3 students. 1 point: 1 student.