Super academic master: start with low adjustment scores!

Solve the problem.

"Find all positive integers x and y such that x^2+3y and y^2+3x are both perfect squares."

Is this problem difficult?

At first glance.

It seems quite simple.

But that's just at first glance.

Bai Yingying thinks that her IQ is not low, and she studies hard, and she is balanced in all subjects, without any shortcomings.

But...

Even so.

When she saw this question, a little star immediately appeared in front of her eyes, and she almost fainted.

Qin Yumo is right.

If you don't have very careful logical thinking and analytical skills, there is no possibility of solving it.

Therefore...

This is a big question with 20 points.

Bai Yingying naturally got a zero.

But Jiangnan got full marks?

So...

While feeling refreshed in her heart.

Bai Yingying also stared at Jiangnan, with a hint of curiosity in her eyes, wanting to see how Jiangnan solved it.

"What?"

"Don't you want to teach me?"

"Do you hate me? Or are you afraid that if you teach me, I will surpass you again in the next exam?"

On the other side, Qin Yumo saw Jiangnan sluggishly sitting in his seat for a long time without moving, and couldn't help but speak angrily.

"Come on!"

"You are destined to be unable to avoid it."

Hearing this, Jiangnan smiled helplessly. Since he couldn't avoid it, he had to explain it!

"Actually, this question is very easy!"

"What do you mean?"

Qin Yumo and Bai Yingying asked at the same time.

"It's nothing more than three situations."

Jiangnan took a pen and made three assumptions on the draft paper.

"First, if x=y."

"Then x^2+3x is a perfect square number."

"Since x^2＜x^2+3x＜x^2+4x+4=(x+2)^2, x^2+3x=(x+1)^2."

"So x=y=1."

"..."

"Second, if x＞y, then x^2＜x^2+3y＜x^2+3x＜x^2+4x+4=(x+2)^2."

"So x2+3y is a perfect square number."

"Because x^2+3y=(x+1)^2, 3y=2x+1, from which we know that y is an odd number."

"Let y=2k+1, then x=3k+1, k is a positive integer, and y^2+3 x=4k^2+4k+1+9k+3=4^2+13k+4 is a perfect square number, and (2k+2)^2=4k^2+8k+4＜4k^2+13k+4＜4k^2+16k+16=(2k+4)^2. ”

“…”

“So y^2+3x=4k^2+13k+4=(2k+3)^2, k=5, and thus x=16, y=11. ”

“If x＜y, x=11, y=16 can be obtained in the same way as x＞y.”

“In summary…”

“(x, y)=(1, 1), (11, 16), (16, 11). ”

“…”

Jiangnan’s thinking is very clear.

Not only is the explanation easy to understand and clear in structure, but it is also done in one go without any pause.

In a few breaths.

He calculated the final answer.

This speed...

It can be said to be fast.

In fact...

Not only Qin Yumo and Bai Yingying were listening carefully.

There were also many students around who stretched their necks, squinted their eyes, and pricked up their ears to look at this scene.

For example, Su Yu, Zhang Hao and Tang Tiantian, as well as Huang Sihai, Hu Dajun and more than a dozen others.

Before, they were threatening Jiangnan and making sarcastic remarks, although they were suppressed by Jiangnan's aura.

But...

This does not mean that they will be convinced.

So when Qin Yumo took the last difficult question on the test paper to ask Jiangnan, their faces were full of jokes.

In their opinion...

Jiangnan cheated in the exam.

Even if he got first place.

But in essence, he was still a poor student.

So Qin Yumo's shameless questioning behavior would make Jiangnan embarrassed and his true colors would be exposed.

But in the end...

Jiangnan easily solved the answer?

Silence!

Deathly quiet.

Everyone around was dumbfounded.

Just because...

Jiangnan explained too fast.

Not to mention Huang Sihai and Hu Dajun, who were ignorant and unlearned, even Su Yu, Zhang Hao, Tang Tiantian, who were academic masters, were confused and couldn't figure it out.

But...

They were sure of one thing.

Jiangnan's answer should be correct.

After all...

Although they didn't understand.

But someone did.

The squad leader Qin Yumo showed a look of sudden enlightenment on his face, and Bai Yingying followed closely.

Obviously...

Both of them understood?

This is indeed the case.

After Jiangnan made threeWhen they made the assumption, Qin Yumo and Bai Yingying knew what to do.

Qin Yumo originally had some doubts about Jiangnan's strength, and this time she asked for advice, there was also a test component.

But now...

She is completely convinced by Jiangnan.

"Jiangnan, thank you!"

"You are really good at math, especially your logical thinking and analytical ability, which is very strong!"

Qin Yumo praised Jiangnan, then hugged the test paper and ran back to his seat excitedly to calculate.

At the same time.

Hearing Qin Yumo's words.

There was a commotion in the classroom immediately.

"This..."

"How is it possible?"

"Is Jiangnan really a top student?"

"He is stronger than everyone in the class, including Qin Yumo, and he was hiding his strength in the past?"

"Maybe we really blamed him wrongly!"

"Nan Shen is worthy of being Nan Shen!"

"66666..."

"..."

At this point, many people who originally doubted Jiangnan immediately changed their attitudes and became respectful.

Of course!

Some people were exceptions.

For example, Su Yu, Zhang Hao, Tang Tiantian, Huang Sihai, and Hu Dajun were unwilling to admit that Jiangnan was excellent.

Their jealousy grew, and their faces became extremely ugly, as if they had eaten dog shit.