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8

Part of 1985 Miklós Schweitzer

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Miklós Schweitzer 1985, Problem 8

Source: Miklós Schweitzer 1985

9/5/2016
Let 25+1≤p<1\frac{2}{\sqrt5+1}\leq p < 1, and let the real sequence {an}\{ a_n \} have the following property: for every sequence {en}\{ e_n \} of 00's and ±1\pm 1's for which ∑n=1∞enpn=0\sum_{n=1}^\infty e_np^n=0, we also have ∑n=1∞enan=0\sum_{n=1}^\infty e_na_n=0. Prove that there is a number cc such that an=cpna_n=cp^n for all nn. [Z. Daroczy, I. Katai]
Miklos Schweitzercollege contestsSequencesdiscrepancy theory