关于 Deutsch、Sagan 和 Wilson 的一个猜想
数论
2007-05-23 v2 组合数学
摘要
我们证明了 Deutsch、Sagan 和 Wilson 近期提出的一个猜想：对于任意素数 p > 3，由前 p 个中心三项式系数模 p 并将非零项替换为 1 所得的有限序列是回文的。补注：该结果此前几乎以相同方式由 Tony D. Noe 证明过：On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7 http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Noe/noe35.html
引用
@article{arxiv.math/0606670,
title = {On a conjecture of Deutsch, Sagan, and Wilson},
author = {Jean-Paul Allouche},
journal= {arXiv preprint arXiv:math/0606670},
year = {2007}
}
备注
This conjecture of Deutsch, Sagan, and Wilson has been already proved in Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7 http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Noe/noe35.html