Dear P.N. Seetharaman

I suggest the following links, have a look:

1. https://www.degruyter.com/document/doi/10.1515/jmc-2016-0018/html

2. https://math.stackexchange.com/questions/24833/is-there-an-elementary-proof-for-fermats-last-theorem

3. https://mathshistory.st-andrews.ac.uk/HistTopics/Fermat%27s_last_theorem/

Best Regards

Dr. Fatemeh Khozaei

You are proving it the wrong way with probability 1.

What a disgrace for a journal to have published that...

P.N. Seetharaman

Preprint OBSERVATIONS ON THE OVERARCHING NATURE OF THE PYTHAGOREAN TH...

"Into the transformed equations we have incorporated the Ramanujan-Nagell equation 2n = 7 + l2which has just five solutions given by (n, ) = {(3, 1); (4, 3); (5, 5); (7, 11); (15, 181)} In this proof, we take is neither a square nor a cube and n is odd".

===================================================

1) 25=7+52=32 for n1=5, l1=5;

2) 215=7+1812, n2=15, l2=181;

3) (25)3=(7+52)3=323=215=7+1812, for n1=5, l1=5, n2=15, l2=181;

4) Thus, 2)=3);

5) So, it is not clear what l numbers ,l1 or l2, and n numbers, n1 or n2, should be used in terms, such as fl(5/3)(1/2).

CONCLUSION: Someone has to use the "trial and error method" over and over again for different numbers n and l to prove FLT?

P.N. Seetharaman https://www.researchgate.net/post/Are_you_interested_in_discussing_controversial_problems_in_mathematics_such_as_FLT_Goldbachs_Problem_Beals_Riemanns_Collatzs_Conjectures_etc

Once again:

Dear P.N.S.,

Thank you for the invitation!

There is no certainty from the very beginning. The presented initial conditions have nothing to do with the presented two equations:

r^p+s^p=t^ p, (1),

x^3+y^3=z^3, (2).

Even if we twist a rope from the initial conditions and tie both equations with them, these conditions will be infinitely far from both of these equations in time and space for one simple reason: these conditions are in no way directly inscribed into these equations. The use of different symbols in different equations, giving the meaning of "prime number" to one of the symbols - all these "tricks" have no meaning for the reason indicated above. Even if you do any spell, it will not give anything new in correcting the above ambiguities.

Consequently, no one can forbid considering the equality of equations among themselves (1)=(2).

For example:

{r^(p/3)}^3+{s^(p/3)}^3={t^(p/3)}^3→x^3+y^3=z^3, where x=r^(p/3), y=s^(p/3), z=t^(p/3).

Sincerely,

SP Klykov

P.S. But, this cannot be something fatal, if you have all this accepted, understood, conscious and make the necessary adjustments. Then you will have a chance.Maybe.

P.N. Seetharaman

Once again:

For Peter Breuer:

"Sergey - we know why z is irrational! He takes x, y integer and x^3+y^3=z^3. A rational z would imply a rational solution (x/z)^3+(y/z)^3=1, and by Holy Euler, there isn't one. "

I understood this as a joke on your part, because the well-known FLT equation x^3+y^3=z^3 for n=3 is in no way connected with the "good wishes" from PNS: "Just for supporting the proof in the above equation, we have another equation x^3+y^3=z^3. Without loss of generality, we assert that both x and y as non-zero integers ". That is, I see the equation: x^3+y^3=z^3. Then, I see the words:" Without loss of generality ... "

Why should someone believe these particular words? Why, for example, can we not write down, for example, words from some popular song? For example,what's about the "Beatles"? How will this change the equation x^3+y^3=z^3?

No changes will take place. For this reason, all grievances from PNS, that someone "did not read the Abstract and did not look at the initial conditions", are groundless.

There is another option, P.N.S. should show how all this "works" in the course of further transformations of all equations. It is not visible. Hence FLT (n=3) and the conditions, which are written next to this equation, are incompatible things yet.

P.N. Seetharaman

And the most important thing. Your logic is not clear. There is no possibilities to say "Excelent!" for incomprehensible logic.

P.N. Seetharaman

Why? Clarify the questions, please. What the problem do you have for this normal situation?

P.N. Seetharaman

"there is absolutely no necessity for me to discuss my paper in future with anyone"

With this, I completely agree!

P.N. Seetharaman

You come up with "designs" that are not listed in the FLT conditions at the very beginning. That is, it is your own invention. It is unknown if these constructs exist.

At the same time, you ignore my question when I write you my own "constructions" that continue your logic:

"{r^(p/3)}^3+{s^(p/3)}^3={t^(p/3)}^3→x^3+y^3=z^3, where x=r^(p/3), y=s^(p/3), z=t^(p/3) "-where is the error here?

You may have noticed that no one rejects this counterargument of mine. Hence, there is no objection.

Until you have an answer to this question, you will not be able to claim something. Perhaps the editors of your journal know the answer to this question if they want to publish the paper? What is the opinion of the editorial board of the journal?

P.N. Seetharaman

I am again giving you a hint.

You must have two different equations with different numbers of terms to avoid the counter-argument that equation (1) = equation (2). Only such a trick will be able to unambiguously separate one equation from another.

Thus:

r^p+s^p=t^p, (1) and

u^3+x^3+y^3=z^3, (2).

But, and in this case someone can ask "why do you think , that

r^p (or s^p) is not equal to u^3+x^3 (or u^3+y^3), for example?"

Therefore, try to use definite equation like:

3^3+4^3+5^3=6^3, (2'). *

Greetings,

* Because, any integer including primes can be expressed using this equation (2').

P.N. Seetharaman

You have been writing in vain for many months that I am "not understanding" something. I understand everything. Moreover, I am one of the few who actually looked through your attempts in detail, starting from April 2021 and found errors. You acknowledged these mistakes and said "thank you" to me. Find this post of yours in the oldest FLT thread?

Now about the essence.

I did not understand the answer to my question and I am repeating it again:

"What happens to the end result if you will not have these words" where p is any prime> 3 "in your text?"

That is, imagine that the above condition is missing. What happens to the result in this case and why?

I have all my today's and most of yesterday's comments deleted today, as I promised. But, I also have copies of them, which can be restored at any time convenient for you.

Are you provoking again? Stop provocations.

P.N. Seetharaman

"Not asking for a hint" and "not using a hint" are completely different things. I already had everything said. And, if necessary, all my materials are saved. I will try not writing here. Be calm.

Chao.

Dears Dr. P.N. Seetharaman and Dr. Sergey P. Klykov ,

Let me consider the last theorem of Fermat (Bur) and Umberto Eco:

The last theorem of Fermat [Bur] with which Simon Singh transformed a "formula" into a "literary case": mathematical proofs [he said] are based on a logical procedure and remain true until the end of time, while Scientific evidence is based on observation and perception, both fallible, therefore sources of "provisional truth" and in any case approximate. If this is really the point, the sales arithmetically demonstrate the question or even the curiosity of the mathematical truths. And on the other hand Umberto Eco, who even recommended it in one of his reviews as a "beach book". The riddle of prime numbers [Bur] written in 2004 by the American mathematician Marcus du Satoy, had somehow agreed in advance: finding the rule to predict the sequence of prime numbers would be the only way to prove, I do not mean the existence but at least to the possibility of God. It may be that mathematics is the true religion and the rest is just superstition .......

see also :

https://www.researchgate.net/post/Where_is_are_my_mistakes_in_the_proposed_approach_for_solving_this_exerciseplease_see_belowand_in_solving_this_exercise

Dear Dr. P.N. Seetharaman

GOD "super partes"

Congratulations Dear Dr. P.N. Seetharaman !!!

Thank you for your words and for your appointment Dear Dr. P.N. Seetharaman. In his book Confessions of a young novelist [2011] Umberrto Eco updated his thesis on Fermat's Theorem [or conjecture] which for him changed as of 1994 thanks to the research work of British mathematician Andrew Wiles.

Thank you very much Dear Dr. P.N. Seetharaman for this important and thoughtful Academic Research.

My best wishes Dear Dr. P.N. Seetharaman !....I wish the best in your progress!

Thank you for your information Dear Dr. PN Seetharaman!

You need more assumptions to say that. In not, just put

x=a^p

r=a^3

for any a

Please, clarify.

Some clarifications.

First.

I can write Eqn.1 is not equal Eqn.2. And it is your problem: to prove is it equal or not...

Second.

Please, remember about p-adic numbers. Since Z is embedded in Zp. There are no even numbers between/among p-adic numbers , there are no odd numbers. There are some primes in some specific Zp and absolute abscence of the same primes in others specific Zp . There are absolute localizations of square roots in some specific Zp and absolute abscence of the same roots in some others specific Zp .

For example, Z7 and Z11:

1. Is the number 5 prime in Z7? Is the number 5 odd in Z7? Both answes are no. Because, we are able to divide 5 by 2:

...(0)57:2=...(3)67.

So, the number 5 is neither prime nor odd (or even) number in Z7.

2. Is number 5 prime in Z11? Is number 5 odd in Z11?

Both the answers are no.

Because, ...(0)511 is divisible by 2 in Z11:

...(0)511:2=...(5)811.

And because, the sqrt[...(0)511]=...4 in Z11.

So, the number 5 is neither prime nor odd (or even) number in Z11.

Apologies. There is no proof and your "NEW OWN METHOD". The real connection between equations 1 and 2 has not been proven. You only have a declaration about one of the two possible connections between them that you can assume. Why are you discriminating against the second possibility? Because of prime numbers and gcd=1? This is unconvincing. If you didn't use a p-adic representation of numbers, it doesn't mean, that such representation doesn't exist. Are you claiming to prove the FLT in its entirety? The article doesn't say,that you are claiming to obtain the proof only in framework of 17th century algebra.

You're welcome! My dear friend.

Hello,

My dear friend.

Sorry, I can't help at the moment, as it was done some times before with my kind advices for you.

Also,I had written about your illusion, about illusory to get proof for the FLT, because you have not yet noticed your hidden error in your "new" variant.

Main reason concludes in your negletion of kind advices.

I wanted to ask about reputated journal, which you had used some days ago to get your new publication after your "Turkish" attempt. What is the result? Are they doing a review?

In any case, I wish you all the best.

Greetings,

P.N. Seetharaman

I would like to interact with any one ,and willing to answer their questions

=====================================

In this case, I would like to ask - where did you lose the seven (digit 7) on your difficult road.

You have at the end of the article:

{s√[(st)p+1]}(E+R)=l2{s√[(st)p+1]}, (1).

Then you wrote:

{s√[(st)p+1]}(E+R-l2)=0, (2).

My questions are following:

1. What will be my (not yours...) mistake, if I will cancel the factors {s√[(st)p+1]} in both parts of the equation (1) and will write following:

equation (E+R)=l2, (3)? Where is my mistake here?

2. There can be no errors in the Ramanujan-Nagell Equation. Therefore, what guarantees can you give , that you did not make the mistake of losing the digit 7 on your difficult path?

This is my simple comment:

Don't you want to check your mistakes by yourself? You invite other people to do it.

I do not know whether it will be possible that someone will take the thankless task of looking for other people's mistakes. But of course, as always, I wish you success!

Sincerely,

Sergey Klykov

P.N. Seetharaman

I think, I have answered your question.

=================================

Yes, you answered. But, I would like to add "almost".

Why? I gave equations where you still don't know that you have 0 or not 0. You write to me now: "...both s and t are non-zero integers." That is, if you have in mind exactly this hypothesis, you have (and MUST do it...)every right to reduce the factors in exactly the same way as I indicated in my first comment today.

At the same time, you keep in mind the exact opposite hypothesis about the presence of 0. (In this case, your reasoning that 5 is not equal to 6 is correct.)

But, this is not the case! You haven't proved yet that the factor {s√[(st)p+1]}=0.

Okay, let's leave it. Could you answer my second question about guarantees? Do you guarantee that the digit 7 is not lost by you?

Sincerely,

Sergey Klykov

Hi,

You could edit you RG account by decreasing of numbers "P.N.Seetharaman" in the

"P.N.Seetharaman P.N.Seetharaman P.N.Seetharaman". It would be saying more in positive direction about your accuracy and can give more trust to you personally and your attempts. This procedure is not hard.

Greetings,

KSP

Preprint SIMPLE PROOF OF THE FERMAT'S LAST THEOREM BY POLYNOMIALS