MathDB

2

Part of 2005 Miklós Schweitzer

Problems(1)

Periodic sequence Related to Golden Ratio

Source: Please Help Me !!!

7/4/2015
Let (an)n≥1(a_{n})_{n \ge 1} be a sequence of integers satisfying the inequality 0≤an−1+1−52an+an+1<1 0\le a_{n-1}+\frac{1-\sqrt{5}}{2}a_{n}+a_{n+1} <1 for all n≥2n \ge 2. Prove that the sequence (an)(a_{n}) is periodic.
Any Hints or Sols for this hard problem?? :help:
number theory unsolvednumber theory with sequencesInteger sequenceperiodic functionirrational numberceiling functionnumber theory