# 夏校申请|2022罗斯数学训练营ROSS申请通道开放！附最新入营测试题

2022年罗斯数学训练营已开放申请。为了保持罗斯营精神的传承，罗斯组委会经过讨论，决定取消线上营。由于疫情防控和出入境管理政策，暂停举办2022罗斯亚洲营。在美国开放两个线下营地，每个营地招收60名新生。受疫情防控和出入境管理政策影响，境外学生可能无法申请美国营。

• 报名方式
登陆官方网站，查看申请所需材料：
https://rossprogram.org
点击网页，进行注册报名：
https://rossprogram.org/students/to-apply/
• 营地时间及费用
俄亥俄州营（多米克大学）
营期：6月15日～7月27日
印第安纳州营（罗斯霍曼理工学院）
营期：6月19～7月29日
• 营地费用
\$6000
• 申请材料
申请者需要在线提交以下申请材料：
1、Background
个人信息
2、Parent Information
家长信息
3、Personal Statement
个人陈述
4、Short Essays
小文书
5、Solutions
申请题
6、Transcript
成绩单
7、Recommendation
推荐信
8、Attachments
附加材料，如简历等
• 招生对象
对数学、科学感兴趣且具备一定英文基础的15~18岁学生

2022年4月1日（美东时间），罗斯数学训练营招生委员会将开始选拔申请者，陆续发放邮件，告知申请者的录取结果。

The number systems Z and Zm (for a positive integer m) were defined in the previous
problem. We also use the notations:
Q is the system of rational numbers.
4Z is the set of multiples of 4 in Z. Similarly for 4Z12.
Consider the following number systems:
Z, Q, 4Z, Z3, Z8, Z9, 4Z12, Z13.
One system may be viewed as similar to another in several different ways.
(a) Let’s measure similarity using algebraic properties. First consider the following
sample properties:
(i) If a2 = 1, then a = ±1.
(ii) If 2x = 0, then x = 0.
(iii) If c2 = 0, then c = 0.
Which of the systems above have properties (i), (ii), and/or (iii)?
(b) Formulate another algebraic property and determine which of those systems have
that property.
Write down some additional algebraic properties and investigate them.
(c) In your opinion, which of the listed systems are “most similar” to each another?