My IQ has been increasing year by year.

July 2nd.

It was exactly 9:00 AM.

The red electric bell on the wall of the university teaching building corridor rang on time.

The ringing lasted for more than ten seconds.

When we stopped, all that remained in the corridor was the continuous chirping of cicadas from the trees outside.

Third floor, fourth examination room.

Before the lecture.

The proctor picked up a paper cutter from the lectern and cut open the seal.

He pulled out a test paper from inside.

"Pass it down from front to back."

The teacher divided the test papers into several parts and handed them to the students in the first row of each column.

Chen Zhuo sat in the second-to-last row by the window.

The person in front of him turned around and handed him the rest of the test paper.

He took it.

Draw one card and hand the last one to the candidate sitting in the last row.

The classroom was instantly filled with the sound of papers being turned over.

On the first problem on the first page.

This is a Diophantine equation with integer solutions.

The problem presents a high-order Diophantine equation and asks for all positive integer solutions.

Chen Zhuo pressed his left hand flat against the edge of the exam paper.

Holding the pen in his right hand, the pen tip landed directly on the answer area.

I wrote a congruence expression on the exam paper.

Using modular arithmetic, we perform parity analysis on both sides of the equation.

Black ink strokes across the white paper, leaving even lines.

He quickly narrowed down the range of values ​​that the variable could take.

Next, through several simple algebraic transformations, the common factor was extracted.

The structure of the equation was broken down.

He listed the last three possible scenarios and verified them one by one.

Write the integer solution at the bottom.

There was no pause.

He turned the page.

My gaze fell on the second polynomial inequality.

This question presents many conditions, with the constraints between several variables intertwined.

Chen Zhuo glanced at the pattern of the coefficients.

He constructed an auxiliary function in the blank space next to the exam paper.

Using Cauchy's inequality, the molecule was subjected to a contraction.

The direction of the inequality sign has changed.

The originally complex algebraic expressions have been stripped of their cumbersome outer shell.

Following the results of the reduction, he wrote down the final step of the proof.

Draw the geometric symbols for the conclusion.

The examination room was quiet, and the air conditioning was blowing a gentle breeze.

Chen Zhuo's answering pace remained steady and calm.

His wrist moved very little; it was just his fingers that controlled the direction of the pen tip.

Time passed by, second by second.

Sunlight streamed in through the glass window on the left, cutting a bright patch of light onto the tabletop.

The exam has been going on for forty minutes.

Chen Zhuo turned to page six of the exam paper.

This is a combinatorial counting problem.

The task is to calculate the number of ways to place a number of pieces on a chessboard with specific rules, satisfying a certain condition that each piece does not attack the others.

Chen Zhuo finally took the blank draft paper.

He did not draw that enormous chessboard.

Instead, he wrote down a few simple recursive symbols on the paper.

He transformed the rules for placing the entire chessboard into a linear recursive sequence.

List the initial values ​​for the first three items.

Then write out the characteristic equations.

Find the eigenvalues.

Rows of calculations appeared on the draft paper.

He substituted the eigenvalues ​​into the template of the general term formula and used the method of undetermined coefficients to find the constants.

The final expression was obtained.

He then wrote down the process logically and clearly in the answer area of ​​the exam paper.

One hour and ten minutes.

Chen Zhuo turned to the last page of his exam paper.

This is the most challenging question on the entire exam paper.

A purely plane geometry proof problem.

No picture provided.

Only a textual description.

Given several fixed points on the circumference of a circle, tangent lines are drawn through these points.

The tangent intersects another secant.

New line segments are then connected between the intersection points.

Finally, prove that the three newly generated intersection points lie on the same straight line.

Chen Zhuo's gaze swept over the text twice.

He pushed the draft paper aside.

Holding the pen in his right hand, the pen tip landed directly on the blank answer area at the bottom of the exam paper.

He abandoned the traditional path of Euclidean geometry.

Complex planes were introduced on the paper.

He defined the core circumcircle in the problem as the unit circle on the complex plane.

In this coordinate system.

The capital letters A, B, and C in the problem represent geometric fixed points.

In Chen Zhuo's writing, they became lowercase plurals a, b, and c.

Because they are all on the unit circle.

Therefore, their conjugate complex numbers are directly equal to their reciprocals 1/a, 1/b, and 1/c.

Chen Zhuo's pen tip moved at a steady speed across the paper.

The black lettering was arranged on the white paper.

Those hidden tangents and secants in the text.

He directly wrote it as an algebraic equation concerning the complex number z and its conjugate complex number z.

Tangent equation.

Secant equation.

Coordinates of the intersection point.

He doesn't need to look for their locations on the map.

All you need to do is put the two algebraic equations together.

Solve for the expression of the intersection point z.

This turned into a purely algebraic calculation problem.

You only need to follow the rules of algebraic operations and deduce step by step.

The fraction line was drawn very straight.

The equal signs should be aligned vertically.

Chen Zhuo's handwriting is very steady.

Where you encounter polynomial multiplication.

He quickly wrote down a few parentheses on the draft paper next to him.

Expand each term, combine like terms, eliminate identical factors in the numerator and denominator, and obtain a clean simplified result.

Then copy this result into the answer area of ​​the exam paper.

There wasn't a single circle or straight line drawn on the draft paper.

It's all letters, fractions, and conjugate symbols.

The ceiling fan overhead was still spinning.

The quartz clock above the blackboard ticked away, its second hand moving one tick at a time.

Chen Zhuo's attention was completely focused on the tip of his pen.

He is working on the final proof that the three points are collinear.

On the complex plane.

To prove that three points are collinear, it is only necessary to prove that the ratio of the complex number formed by these three points is a real number.

A complex number is a real number if and only if it is equal to its conjugate complex number.

Chen Zhuo wrote a long fraction on the exam paper.

The numerator and denominator of the fraction contain the complex expressions of all the previously calculated intersection points.

It has many letters and a long structure.

He began to find the conjugate of this fraction.

This is a tedious and cumbersome calculation process.

Substitute.

Unfold.

Tongfen.

Chen Zhuo's wrist moved steadily across the exam paper.

List out the formulas line by line.

With the final step of simplifying the fraction completed.

The complex numerator and denominator cancel each other out.

On the right side of the equal sign, a form exactly the same as the original fraction appears.

Chen Zhuo added a period at the end of the equation.

The proof is complete.

He put down his pen.

He looked up and glanced at the clock hanging above the blackboard.

10:20.

There is one hour and forty minutes left until the end of the exam.

The spots of sunlight shining on the desk have shifted.

The air in the examination room became somewhat stuffy.

Chen Zhuo put down his pen.

He turned the test paper back to the first page.

I scanned the admission ticket number I had filled in from beginning to end.

Make sure there are no missing spaces.

He put the eraser and pen back into his pencil case.

Zip up the zipper.

Push back the chair and stand up.

The chair was pulled on the ground with a short, sharp sound.

Chen Zhuo picked up the test paper and draft paper on the table.

Pick up your admission ticket and ID card from the top left corner, and take your stationery bag.

He walked out from the aisle between the desks.

He walked to the front of the classroom.

Place the exam paper and draft paper flat on the teacher's desk.

The teacher sitting at the back of the classroom looked up.

He glanced at Chen Zhuo, then at the clock on the wall.

The teacher lowered his head and looked at the test paper that Chen Zhuo handed in.

The exam paper was turned to the last page, where the most challenging question was located.

The blank answer area was filled with writing.

The above are all neatly arranged complex equations.

The teacher paused for a moment, his gaze following the derivation steps.

I saw the definition of a unit circle.

I saw the expression for the intersection point.

I saw the final proof that the real numbers are equal.

The teacher looked up at Chen Zhuo.

Chen Zhuo stood calmly in front of the speaker.

The teacher collected the test papers and placed them under a transparent folder.

Chong Chenzhuo nodded slightly.

Chen Zhuo nodded as well.

He turned and walked towards the back door of the classroom.

He opened the door and went outside.

The door closed behind me.

The corridor was deserted.

Only a few tall sycamore trees outside the window, their branches and leaves swaying in the breeze.

Chen Zhuo walked down the stairs.

The lobby on the first floor was somewhat dimly lit.

He pushed open the glass door on the ground floor of the teaching building.

The sunlight poured down at 10:30 a.m.

The glaring light made him squint slightly.

A wave of heat hit us, and swirling steam rose from the asphalt road.

The air was still very humid, mixed with the smell of leaves.

In front of the teaching building is a spacious plastic track and field.

A red running track, a green lawn.

Chen Zhuo walked along the path in front of the woods at the edge of the playground.

Walk to a small shop at the end of the playground.

There are two vending machines against the wall.

He stopped in his tracks.

He took a few coins out of his pocket.

Insert the coin into the slot.

The coins rolled down the track, making several metallic clanging sounds.

Press the button.

The sound of the vending machine running could be heard from inside.

A can of chilled cola fell onto the pickup slot.

Chen Zhu bent down and took it out.

He took the Coke and walked to an old sycamore tree.

The tree trunk was thick, and a peeling wooden bench sat in the shade.

Chen Zhuo sat down on the bench.

The pencil case and exam admission ticket were placed on the empty space next to me.

He held the pull ring with one hand.

Pull it upwards with force.

A blast of cold air, accompanied by the sound of carbonated bubbles, emerged.

He tilted his head back and took a big gulp of iced cola.

The icy liquid rushed into my stomach.

Chen Zhuo put down the can.

Leaning back against the hard wooden back of the bench.

Place your hands on your knees.

Looking at the empty playground in front of me, and at the glass windows of the teaching building in the distance.

The sound of cicadas swirled overhead.

Occasionally, a warm breeze would blow by.

He sat quietly on the bench, waiting for the exam to end.

The angle of the sunlight gradually shifted, and the shadows on the bench shortened somewhat.

The rubber track on the playground emitted a slightly scorching smell under the high temperature.

Time passed by, second by second.

It's exactly twelve o'clock.

The loudspeakers on the campus radio were emitting a static sound.

Then, a rapid ringing of the handover bell echoed throughout the school.

"The exam is over. Please stop answering the questions."

An electronic announcement came over the loudspeaker.

The teaching building was quiet for a few seconds.

The classroom doors on each floor were pushed open.

People began to pour out down the stairs.

A few minutes later, the entrance to the teaching building was filled with examinees.

The coaches leading the team stood outside the cordon.

Chen Zhuo sat on the bench, looking at the crowd.

He finished the last sip of cola in the can.

Throw the crushed empty can into the trash can next to it.

It made a loud "danglang" sound.

He picked up the stationery bag and exam admission ticket next to him.

I stood up and walked along the path in front of the forest towards the school gate.

in the crowd.

He saw a red folding umbrella and several backpacks that Coach Xu was holding.

Chen Zhuo approached the cordon.

Zhou Kai is already standing next to the coach.

He was carrying a schoolbag, and his hair was damp with sweat, sticking to his skin.

Lin Yi squeezed through the crowd, walked to Chen Zhuo's side, and leaned against the railing of the cordon.

I waited a while longer.

Zhang Bai, Mo Xiaoyu, and Li Nanbai slowly walked out with the flow of people.

All three of them looked pale, showing signs of exhaustion from prolonged and intense mental exertion.

No one spoke.

Coach Xu looked at them.

Put away the red umbrella in your hand.

"The exam is over, that's it. Keep your admission ticket safe."

Li Nanbai let out a long breath.

He reached out and rubbed his stomach.

What should we eat for lunch?

"Eat something that's not so sweet."

Chen Zhuo casually replied.

Coach Xu pointed to the street outside the school gate.

"Let's go back and find a place with air conditioning first, have a good lunch, rest in the afternoon, and then I'll take you to Shanghai for a look around." Chen Zhuo stuffed the pencil case into the backpack that Coach Xu was helping to carry.

Carry it over one shoulder.

I started walking and followed.

The summer sun was still blinding.

The shadows of the seven people stretched long on the asphalt road.