This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND:
OR:
NO:

Found problems: 1

1985 Miklós Schweitzer, 8
Tags: discrepancy theory , sequence
Let $\frac{2}{\sqrt5+1}\leq p < 1$, and let the real sequence $\{ a_n \}$ have the following property: for every sequence $\{ e_n \}$ of $0$'s and $\pm 1$'s for which $\sum_{n=1}^\infty e_np^n=0$, we also have $\sum_{n=1}^\infty e_na_n=0$. Prove that there is a number $c$ such that $a_n=cp^n$ for all $n$. [Z. Daroczy, I. Katai]