As a Grind King-level student who studied 14.4 hours every day, Xiao Yi had developed the habit of thinking through problems in his head even while eating or walking.
Of course, for him, studying in his head was merely a way to keep his BUFF going. It was nowhere near as rewarding as reading directly or solving actual problems.
After all, his purpose in studying was ultimately to gain more knowledge. Maintaining the buff was simply something he did along the way.
So when he spotted a math problem written on a small blackboard halfway down the corridor, it was naturally irresistible to him.
It was like running into a wild experience pack on the road. Who would leave a pack lying there unclaimed?
And besides...
This wild experience pack looked pretty high-quality.
"Hmm... The problems from the past two days were both quite difficult. They were probably the hardest problems I'd encountered in all my time studying."
As Xiao Yi walked toward the small blackboard, he thought to himself.
Before this, he had only done questions from worksheets handed out by teachers, exercise books, and reference books like Wu San that he had bought himself. Yet not a single one of those problems had stumped him. They had even begun to bore him terribly.
Then, after dinner the day before yesterday, he had passed by this place and happened to glance over. He saw a math problem on the board and was delighted to discover that it was a type of problem he had never done before—quite difficult, too!
It had taken him a full three minutes to come up with a solution!
That excited him. It was clearly far more interesting than the problems in exercise books, which took him less than half a minute at most.
"Especially yesterday's problem. It was even harder than the one from the day before yesterday. It took me nearly five minutes to finish it. I wonder whether today's problem will be even harder."
At that thought, Xiao Yi was already growing impatient with anticipation.
He quickened his pace, swiftly reached the small blackboard, and looked at the problem written on it.
Find all positive integers n such that there exists P(x) ∈ Z[x] with the property that, for every positive integer m, p^(m)(1), p^(m)(2), ..., p^(m)(n), when divided by n, have exactly ⌈n/2^m⌉ distinct remainders, where p^(m) denotes the m-th iterate of p.
The moment Xiao Yi saw the problem, his eyebrows rose.
"Eh... This problem seems..."
Very interesting?
In terms of difficulty, Xiao Yi could say with certainty that it was many levels harder than the problems from the previous two days.
As for its type, it was completely different as well—another kind of problem he had never encountered before.
Even the information provided in the statement was rather obscure in mathematics textbooks, the sort of thing that rarely appeared.
For example, the ceiling notation "x," and the concept of iteration.
At least... as a second-year high school student, he had never learned such things in class.
Remembering that this was the Senior Year Department, he could not help sighing to himself. "So senior students have to face problems at this level."
No wonder they were powerhouses of the senior year realm!
With the college entrance examination just ahead of them, even their problems were this challenging.
For a moment, he could not help looking forward to his own senior year. How happy would he be if he could solve problems like this every day?
Xiao Yi: (▽).
After being happy for a moment, he quickly put those thoughts aside and began studying the problem seriously.
Although he had basically never learned this knowledge in class, all of it had appeared in the dozen or so mathematics books he had already finished reading.
So he could fully understand what the problem was asking.
Then, he began seriously considering how to solve it.
A storm of thought quietly unfolded in his mind. The effect of the tenth level of Ruthless Continuous Study began to take effect at that moment.
Naturally, no one else could see those "storms."
Meanwhile, at the other end of the corridor.
"Is it this student?"
Liu Bin narrowed his eyes and stared intently through his reflective lenses at the student standing before the small blackboard.
Beside him, Chen Liang also watched the student while trying to recall whether there was anyone in the entire senior year with exceptional math grades who matched this person.
Unfortunately, he could not think of anyone.
"I don't know. Let's watch first. He looks like a second-year student."
But Liu Bin was already walking over. "Come on, let's go take a look."
Chen Liang stopped Liu Bin. "Let's watch for now. If he isn't the student we're looking for, the real student might not come over if he sees us standing there."
Liu Bin considered it, then nodded. "That makes sense."
Returning to his original spot, he folded one arm across his chest and pinched his chin with the other. "If it really is this student, I'm curious how long he'll need to solve this problem."
Chen Liang said, "Didn't you say this problem was harder than the previous two problems combined? Maybe it'll stump this student."
Liu Bin smiled. "That's possible too."
"This is a difficult problem I carefully selected. You know about IMO Preliminary Problems, right?"
Chen Liang nodded. "Yes. Every year, math olympiad problem-setting teams from various countries send problems to the International Mathematical Olympiad organizing committee. The committee then selects some as preliminary problems for students from different countries to train on for the following year."
"Exactly." Liu Bin nodded. "And this problem is the hardest among this year's IMO Preliminary Problems. It could even rank among the hardest in IMO history. It's far more difficult than those chosen as official IMO problems."
"To put it simply, the problem was too difficult, so it wasn't selected as an official problem."
Chen Liang's eyes widened. "That absurd?"
"It really is that absurd." Liu Bin nodded, then raised an eyebrow. "So this student may really be unable to solve it. Even if he can, I'd estimate at least half an hour... An hour isn't impossible."
Chen Liang nodded.
However, at that moment, something even more absurd happened. They saw the student standing in front of the small blackboard pick up a piece of chalk from beside it and begin writing.
The opening character, "Solution," immediately let them recognize that this student had to be the mysterious student from the previous two days!
Liu Bin no longer hesitated and walked straight over. Chen Liang hurried after him.
Behind them, several other senior-year teachers followed as well.
After all, who would not be curious about this mysterious student?
Thus, their group made its way over in a grand procession.
However, since they were still some distance from the small blackboard—nearly the entire length of the corridor—it would take them a while to reach it.
As they walked over, they watched the student smoothly write out the solution step by step.
There was not even the slightest pause in the middle.
Finally, they arrived in front of the blackboard.
And at that very moment, the student had finished writing the solution and added the period that marked its end.
Liu Bin looked at the solution, and his gaze froze.
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