Ouye enters the defense meeting and projects her doctoral dissertation onto the screen.

"Professor Flamont, Professor Nummenberg, Professor Hanks, good afternoon. Ou Ye said politely, glancing at Shen Qi and Lyndon Strauss in the audience.

The main respondent, Professor Flammont, had a poker face, and he said without a smile: "Oh, this is the fourth semester of your doctoral program. ”

Ou Ye nodded: "Yes." ”

Professor Flamont was stern, and Shen Qi sweated for Ou Ye.

However, Ou Ye played smoothly after entering the market, and he did not miss it, which is a good sign.

Professor Flamont: "Oh, your doctoral dissertation, "The Proof of the Jesmanovich Conjecture", has been read by our three respondents, and you will make a presentation for 3 to 5 minutes, and then we will ask questions. ”

Oye: "Okay. ”

3 to 5 minutes of presentation?Shen Qi was a little surprised, under normal circumstances, the opening presentation time of doctoral students is between 15-20 minutes.

Lyndon Strauss turned his head and smiled, his eyes told Shen Qi: We are very tolerant, and it varies from person to person.

Ouye holds a flip pen in her hand and switches the PPT of her doctoral dissertation

Oye cuts to page 3: "This, Lucas sequence. ”

Ouye does not stop on page 4 and cuts directly to page 5: "This, Lucas even, equivalent." ”

The PPT page number shows that there are 101 pages, and Ou Ye averages a page in 5 seconds.

The three respondents did not raise any objections, and quietly watched Ou Ye quickly brush PPT.

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 main point of making a PowerPoint presentation is to highlight the key points of each page, and the presenter of the PowerPoint presentation must express the strongest point of view in the most concise language in a limited time.

Ou Ye's PPT expression is refined to the extreme, 101 pages, she finished the statement in 5 minutes, and the language expression style is similar to usual, only the key points are not grinding.

"OK, thank you for your statement, Ou, and let's move on to the question session. Professor Flamont was the first to ask, and he said: "You just mentioned the Lucas sequence, and in the paper it is defined as un=un(α,β)=α^n-β^n/α-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 find the primordial divider of un(α,β) in reverse?"

Professor Flamont's question is a trap...... Shen Qi has gone through the printed version of Ouye's paper, and it is a logical trap to find the primordial divider of un(α,β) in reverse, because un(α,β) does not have the primordial divider.

Ouye was conscious and responsive, and she replied, "I can't find it." ”

Professor Flamont asked, "Why?"

Ou Ye switched PPT to page 13, and the laser irradiation of the operating page-turning pen was un(α1,β1)=±un(α2,β2), and synchronously explained: "It does not have, the primordial divider." ”

"Really? are you sure?" Professor Flamont continued.

"I'm sure. "Oye is extremely determined.

"Now for Professor Noumenberg and Professor Hanks. Professor Flamont stopped asking, and he looked down and wrote and drew on the defense transcript.

Professor Nummenberg, who has a round face, a bald head, and a smile that looks like a white version of Maitreya Buddha, asked, "Oh, I don't really understand what is the basis for you to take 5≤n≤30 and n≠6?"

"Hmm. Ou Ye was prepared, she switched the PPT to page 39, and the striking focus of this page is the equation (11):(2k+1)^x±(2k(k+1)))^y√-2k(k+1)=±(1±√-2k(k+1))^z

"Given a positive integer k, there is no solution to a positive integer of z≥3. Ouye said.

"OK, I don't have a problem for the time being. Professor Nummenberg bowed his head to record, presumably grading Oye.

The second question was asked and answered for only a minute, but Shen Qi, who was listening, knew that this question was by no means as simple as it seemed.

If (x,y,z) is a positive integer solution of equation (11), then 1+√-2k(k+1) and 1-√-2k(k+1) form Lucas even.

A new equation can be obtained from equation (11), which is equation (12) in Euye's paper, which can verify that uz(1+√-2k(k+1), 1-√-2k(k+1)) have no primordial factor.

From the BHV theorem, there is no positive integer solution (x,y,z) of z≥3, and back to the premise definition, if un(α,β) does not have an primordial divider, then n must take 5≤n≤30 and n≠6.

Logically, Ouye's answer "given a positive integer k, no z≥3 positive integer solution" belongs to the nature of a final conclusion, and she understands this logic in her heart, so that she can summarize the core conclusion derived from this logic in one sentence.

Let Ou Ye talk about the full set of derivation logic at length, then she will have to talk about it all day.

Fortunately, this is Princeton, and the three respondents have studied Oye's thesis beforehand, they are all famous mathematics professors, and one or two key defense sentences from the respondent are enough for the three respondents to give a score.

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

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

Shen Qi was stunned, what the hell is Ryan's principle?

Professor Lyndon Strauss was stunned, z must be 2, z can only be 2 and cannot take 1! Ouye's conclusion is confirmed by me, and it will not be wrong!

Only when the condition of z=2 is satisfied, substituting the previous equation, can it be proved that only the integer solution (x,y,z)=(2,2,,2), that is, the complete proof of the Jesmanovich conjecture is true.

Professor Hanks' calculation based on Ryan's principle of z=2 or 1, if true, would overturn Oye's doctoral dissertation, and the Jesmanovich conjecture has still not been fully proven, and the work that Oye is doing now is not fundamentally different from the work that Jesmanovich himself did decades ago.

Ou Ye was anxious, her face turned white and red, she clenched her fists and argued 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 satisfying the algebraic integer ring! On both sides of equation (22) modulo 2 (n + 1) to get 2 ∣x, modulo 2 n (n + 1) + 1 to get 4 ∣x, and so on, we must rule out the case of z = 1, so z can only take 2!"

Oye suddenly erupted, startling the three respondents, and Professor Hanks's pen accidentally fell to the ground.

"This ...... Runaway little Yezi?" Shen Qi was also frightened, he had never seen Ou Ye so excited, this was probably the longest passage that Ou Ye said in one breath after he got sick, it was reasonable, well-founded, and quite 6.