After deciding that the next research direction was number theory, and the topic was about the Erdős arithmetic sequence conjecture, Zhao Xiancai continued to read and searched online for some previous research on the Erdósh arithmetic sequence conjecture.

.

Once a question is raised, as time goes by, more or less people will participate in it and leave their research results.

The amount of research results on these problems is not only related to the difficulty of the problem, but also related to its popularity.

If the popularity is high, then those who study it will probably gain more fame, fortune, or money after they achieve results, and naturally there will be many more people studying it than those who study unpopular problems.

If more people study some problems, they may take different paths. These paths may seem to lead to the end, but they may really just appear. If this path goes dark, it may always be the same.

No results.

Latecomers can either open up new paths on their own, or continue along the path of their predecessors until the problem is solved.

In the process of learning about it through the Internet, Zhao Xiancai also learned that as early as 2004, Tao Zhexuan and Ben Green had proved a weakened version of Erdös's arithmetic sequence conjecture.

People began to think about the question "are there infinitely many prime numbers" a long time ago, and more than two thousand years ago, people knew that the answer to this question was that there are infinitely many prime numbers.

Regarding this conclusion, Euclid left behind a classic proof by contradiction.

After solving this problem, another problem arises.

Since there are infinitely many prime numbers, are there also infinitely many prime numbers in the arithmetic sequence?

Dirichlet's theorem provides a proof for this problem. It shows that for any mutually prime positive integers a and d, there are infinitely many prime numbers in the form a nd, where n is a positive integer, that is, in the arithmetic sequence a d,

There are infinitely many prime numbers in a 2d, a 3d,...

Since there are infinitely many prime numbers in the arithmetic sequence, is there an arithmetic sequence of prime numbers of any length?

Tao Zhexuan and Ben Green gave the answer to this question, that is, yes, so this is also called the "Green-Tao Theorem".

However, the Green-Tao theorem only proves the existence, and it is still very difficult to find a specific arithmetic prime number sequence.

"This conjecture has few premises and strong conclusion. If you buy it directly from the system with points, it will cost more than 50,000 points. There is no teaching yet, so you can only read the papers provided by the system.

Now it seems that I can only do some research on my own for a while. Anyway, the task requirement is before graduating from college. Although I asked the system, the system replied that the university mentioned here is only for undergraduates, but it will still take a few years.

If this conjecture can be proven or disproven by me, whether it is a top journal or an international mathematics award, it will be settled."

When the time came to August 10, Zhao Xiancai had already read a lot of papers related to Erdös' arithmetic sequence conjecture. After reading another paper that afternoon, he thought so in his mind.

In fact, the choice of Erdős's arithmetic sequence conjecture is also related to the fact that Zhao Xiancai was more interested in this type of problem during the previous mathematics competition.

He took so many mathematics exams before going to college. Although there were no questions that could really stump Zhao Xiancai in the later stages, for him, number theory problems were still what he was best at and most interested in.

Since it was determined that the next research content would be about Erdős's arithmetic sequence conjecture, Zhao Xiancai's daily schedule was to read books in the morning and evening to learn new knowledge, and to find and read relevant papers and materials in the afternoon.

During the more than a month since he returned to Chengxian from the capital during the summer vacation, Zhao Xiancai had almost never left the house except for one trip when he had dinner with his high school classmates. At this time, his hair had also

It's grown a lot longer.

"You're going to school for military training in a few days, right?

Look at your hair. It's so long. Remember to shave it before you leave.

It’s such a hot day, you’re not afraid of the heat even if you have such long hair.”

During dinner in the evening, Zhao Xiancai's mother said to him.

"Mom, no need, the school will give us a uniform haircut during the military training later," Zhao Xiancai said.

This long hair is a bit of a hindrance. Not only can I often see my hair on the bed and on the floor at home, but sometimes it even covers my eyes.

However, it was only a few days before the military training started, and Zhao Xiancai was too lazy to run to town. He might as well read one more paper at home during this time.

Zhao Xiancai's mother now only talks to him about things in life. She can't say anything about studies even if she wants to. After all, the English papers Zhao Xiancai reads at home every day are dazzling to her after just one glance.

From August 16 to 29, 2015, it was the time for Zhao Xiancai and his group of 2014 undergraduates to undergo military training. Zhao Xiancai had told his parents before this time, and they remembered it quite clearly.

All training students need to return to school on August 13th, so Zhao Xiancai and Chengxian left on the 13th.

Afterwards, military training uniforms were distributed at noon on the 14th, and a military training mobilization meeting was held on the morning of the 15th. Hair was trimmed throughout the day and military training materials were prepared. Zhao Xiancai also shaved his hair short on this day.

As for preparing military training materials, Zhao Xiancai and the others need to bring their own lunch boxes and tableware because the canteen at the military training base does not provide plates and cutlery.

In addition, there are toiletries, care products, washing supplies, sports shoes, other clothing, etc., which you need to bring.

"I heard from some seniors that due to the limited conditions of the military training base, the conditions for bathing are not very good. After 14 days of military training, each person only went to the bathhouse to bathe 3 to 5 times."

On the afternoon of the 15th, when everyone was preparing military training materials, Zhang Qiuyu said.

"Only 3 to 5 baths in 14 days? Damn it, on such a hot day, even if you take more than 5 baths per person, 14 days is about once every three days. It really won't stink.

?"

After hearing Zhang Qiuyu's words, several people in Zhao Xiancai's dormitory also looked shocked.

"It stinks, why doesn't it stink, but there's nothing you can do about it, that's the rule. The seniors said that when they are not allowed to take a bath, they usually wipe their bodies with cold water to try to wipe away the stinky sweat they shed throughout the day.

There are a lot of troubles in this military training. The time for bathing in the bathhouse is still short, so you have to hurry up when washing. It would be terrible if the water stops halfway and there is still shower gel on the body.

besides……"

Zhang Qiuyu began to tell Zhao Xiancai and others various military training stories he had heard from his seniors and some of their seniors' coping methods.

…

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