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arXiv · 0812.1724

On Bialostocki's conjecture for zero-sum sequences

Song Guo·Zhi-Wei Sun
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Abstract

Let $n$ be a positive even integer, and let $a_1,...,a_n$ and $w_1, ..., w_n$ be integers satisfying $\sum_{k=1}^n a_k\equiv\sum_{k=1}^n w_k =0 (mod n)$. A conjecture of Bialostocki states that there is a permutation $σ$ on {1,...,n} such that $\sum_{k=1}^n w_k a_{σ(k)}=0 (mod n)$. In this paper we confirm the conjecture when $w_1,...,w_n$ form an arithmetic progression with even common difference.

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Song Guo, Zhi-Wei Sun. 2009-12-16. On Bialostocki's conjecture for zero-sum sequences. https://doi.org/10.4064/aa140-4-3

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