Ou Ye entered the defense meeting and projected her doctoral thesis onto the screen.

"Professor Flamont, Professor Numanberg, Professor Hanks, good afternoon." Oye said politely, glanced at Shen Qi and Linden Strauss in the audience.

Professor Flamont, the chief defense officer, had a poker face. He said seriously: "Oh, this is your fourth semester of doctoral students."

Ou Ye nodded: "Yes."

Professor Flamont is a harsh person, and Shen Qi is worried about Ou Ye.

However, Ou Ye performed smoothly after entering the court, and there was no slightest sign, which is a good sign.

Professor Flamont: "Ou, your doctoral thesis "Proof of the Jesmanovich Conjecture", has been read by our three defense officers. You will make a statement for 3 to 5 minutes next, and then we will ask questions."

Ou Ye: "Okay."

A statement of 3 to 5 minutes? Shen Qi was a little surprised. Under normal circumstances, the opening statement time of a doctoral student is between 15 and 20 minutes.

Linden Strauss turned his head and smiled. His eyes told Shen Qi: We are very tolerant, and they vary from person to person.

Ou Ye holds a page turner pen and switches her ppt in her doctoral thesis

Oye cut to page 3: "This, Lucas sequence."

Ou Ye did not stop on page 4, but cut directly to page 5: "This, Lucas even number, equivalent."

The ppt page number shows 101 pages, and the Ou Ye passes one page in an average of 5 seconds.

The three defense officers did not raise any objection, but watched Ou Ye quickly brushing ppts.

poer-point, this is the real ppt... Shen Qi has never seen such a concise ppt report, and the essence of ppt is exactly this: a strong point of view.

The key point of making ppt is to highlight the key points of each page. PPT reporters must use the most refined language to express the strongest views within a limited time.

Ou Ye’s PPT expression is refined to the extreme. She finished her statement in 5 minutes on page 101. Her language expression style is similar to usual, and she only talks about the key points without slacking off.

"Ok, thank you for your statement, Ou, let's go to the questioning session next." Professor Flamont asked first, and he said: "You mentioned the Lucas sequence just now and defined it in the paper as un=un(a,β)=a^n-β^n/a-β, where n is a positive integer. This definition is fine, this is the premise. So what I want to ask is, based on this definition premise, how to reversely find the original element denominator of un(a,β)?"

Professor Flamont's question is a trap... Shen Qi has gone through Ou Ye's printed version of the paper and indirectly finding that the original element derivation of un(a,β) is a logical trap because un(a,β) does not have the original element derivation.

Ou Ye was sober and sensitive, and she replied: "You can't ask for it."

Professor Flamont asked: "Why?"

Ouye switches ppt to page 13, operates the page turner to irradiate the laser light to un(a1,β1)=±un(a2,β2), and explains simultaneously: "It does not have it, and the original element is eliminated."

"Is that so? Are you sure?" Professor Flamont continued to ask.

"I'm sure." Ou Ye was extremely firm.

"The following is a question from Professor Numanberg and Professor Hanks." Professor Flamont stopped asking questions, and he lowered his head and wrote and painted on the defense record paper.

Professor Numanberg had a round face, bald head, and smiled like a white version of Maitreya Buddha. He asked: "Oh, regarding Lemma 1, I don't really understand what the basis for you to take 5≤n≤30 and n≠6?"

"Yeah." Ou Ye was prepared for a long time, and she switched ppt to page 39. The eye-catching focus of this page is equation (11): (2k+1)^x±(2k(k+1))^y√-2k(k+1)=±(1±√-2k(k+1))^z

"Given the positive integer k, there is no positive integer solution with z≥3." said Ou Ye.

"Ok, I have no problem for the time being." Professor Numanberg lowered his head to record, probably giving Ou Ye a score.

The second question can only be answered for a minute, but Shen Qi, who was listening, knew that this question was not as simple as it seemed.

If (x, y, z) is the positive integer solution of equation (11), according to the premise definition, we can know that 1+√-2k(k+1) and 1-√-2k(k+1) form Lucas even numbers.

From equation (11), we can obtain a new equation, namely the equation (12) in Euye paper, and we can verify that uz(1+√-2k(k+1), 1-√-2k(k+1)) has no original factor.

From the bhv theorem, we can find that there is no positive integer solution (x, y, z) with z≥3. Return to the premise definition, if un(a, β) does not have the original divisor, n must take 5≤n≤30 and n≠6.

Logically, Ou Ye's answer "Given a positive integer k, no positive integer solution with z≥3" is a conclusive nature. She understands this logic in her heart, so she can summarize the core conclusion derived from this logic in one sentence.

If Ou Ye talks about the complete set of derivation logic in a long and long way, she will have to talk about it all day long.

Fortunately, it was Princeton here, and the three defense officers had studied Ou Ye's paper in advance. They were all famous mathematics professors. Yi Ye Zhiqiu, and the respondent's one or two key defense words were enough to get the three defense officers to give scores.

At this time, Professor Hanks spoke: "Let me say a few words, Ou, you prove that z≥3 does not exist, that is, z is either 1 or 2, your final conclusion is z=2. And I calculated based on Ryan's principle that z can take 1 or 2, so I think your proof of the Yesmanovich conjecture is not valid."

As soon as this question came out, Ou Ye was stunned: "..."

Shen Qi was shocked, what the hell is Ruian's principle?

Professor Linden Strauss was shocked. Z must be 2, z can only be 2, and 1 cannot be taken! I have confirmed Ou Ye's conclusion and will not be wrong!

Only when the condition of z=2 is satisfied and substituted with the previous equation can we prove that the equation a^x+b^y=^z has only integer solution (x,y,z)=(2,2,,2), that is, the complete proof of the Yesmanovich conjecture is true.

Professor Hanks calculated z=2 or 1 based on Ryan's principle. If this conclusion is true, it will overturn Oye's doctoral thesis. The Yesmanovich conjecture still cannot be fully proved. The work Oye is doing now is no essential difference from the proof work that Yesmanovich himself decades ago.

The results I have worked hard for two years should not be overturned! Ou Ye was anxious, her face turned pale and red, and she clenched her fists and debated loudly: "Professor Hanks, please look at pages 92 to 101 of my paper. For any (x, y, z) in s, there is a unique rational number l that satisfies the algebraic integer ring! On both sides of equation (22), modulo 2 (n+1) gets 2ix, then modulo 2n(n+1) + 1 gets 4ix, and so on, we can definitely rule out the situation of z=1, so z can only take 2!"

Ou Ye suddenly broke out, and the three defense officers were startled. Professor Hanks' pen accidentally fell to the ground.

"This... the rascal little Ye?" Shen Qi was also frightened. He had never seen Ou Ye so excited. This was probably the longest sentence Ou Ye said in one breath after he got sick. It was reasonable, truthful and truthful, quite 6.
Chapter completed!