元素构建游戏在\（\mathbb{Z}_n\)
Q3 Mathematics
引用次数: 0
摘要
我们考虑一对游戏，其中两个玩家交替选择先前未选择的\（\mathbb）元素{Z}_n\)给定特定的起始元素。在每个回合中，玩家将他们选择的元素与上一回合的结果相加或相乘。在一场比赛中，如果最终结果为0，则第一名选手获胜；在另一种情况下，如果最终结果为0，则第二个玩家获胜。当\（n\in\｛2p，4p \｝\）为某个奇数素数p时，我们确定除了后一个具有非零起始元素的博弈之外，哪一个博弈对两个博弈都有获胜策略。本文章由计算机程序翻译，如有差异，请以英文原文为准。
Element-Building Games on \(\mathbb {Z}_n\)
We consider a pair of games where two players alternately select previously unselected elements of \(\mathbb {Z}_n\) given a particular starting element. On each turn, the player either adds or multiplies the element they selected to the result of the previous turn. In one game, the first player wins if the final result is 0; in the other, the second player wins if the final result is 0. We determine which player has the winning strategy for both games except for the latter game with nonzero starting element when \(n \in \{2p,4p\}\) for some odd prime p.
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来源期刊
Arnold Mathematical Journal
Mathematics-Mathematics (all)
CiteScore
1.50
自引率
0.00%
发文量
28
期刊介绍：
The Arnold Mathematical Journal publishes interesting and understandable results in all areas of mathematics. The name of the journal is not only a dedication to the memory of Vladimir Arnold (1937 – 2010), one of the most influential mathematicians of the 20th century, but also a declaration that the journal should serve to maintain and promote the scientific style characteristic for Arnold''s best mathematical works. Features of AMJ publications include: Popularity. The journal articles should be accessible to a very wide community of mathematicians. Not only formal definitions necessary for the understanding must be provided but also informal motivations even if the latter are well-known to the experts in the field. Interdisciplinary and multidisciplinary mathematics. AMJ publishes research expositions that connect different mathematical subjects. Connections that are useful in both ways are of particular importance. Multidisciplinary research (even if the disciplines all belong to pure mathematics) is generally hard to evaluate, for this reason, this kind of research is often under-represented in specialized mathematical journals. AMJ will try to compensate for this.Problems, objectives, work in progress. Most scholarly publications present results of a research project in their “final'' form, in which all posed questions are answered. Some open questions and conjectures may be even mentioned, but the very process of mathematical discovery remains hidden. Following Arnold, publications in AMJ will try to unhide this process and made it public by encouraging the authors to include informal discussion of their motivation, possibly unsuccessful lines of attack, experimental data and close by research directions. AMJ publishes well-motivated research problems on a regular basis. Problems do not need to be original; an old problem with a new and exciting motivation is worth re-stating. Following Arnold''s principle, a general formulation is less desirable than the simplest partial case that is still unknown.Being interesting. The most important requirement is that the article be interesting. It does not have to be limited by original research contributions of the author; however, the author''s responsibility is to carefully acknowledge the authorship of all results. Neither does the article need to consist entirely of formal and rigorous arguments. It can contain parts, in which an informal author''s understanding of the overall picture is presented; however, these parts must be clearly indicated.
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