I cordially invite mathematicians to offer their valuable comments on my paper.

Wiles's proof of Fermat's Last Theorem is a proof by British mathematician Andrew Wiles of a special case of the modularity theorem for elliptic curves. Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Wiles first announced his proof on Wednesday 23 June 1993 at a lecture in Cambridge entitled "Modular Forms, Elliptic Curves and Galois Representations". Wiles's proof uses many techniques from algebraic geometry and number theory, and has many ramifications in these branches of mathematics. It also uses standard constructions of modern algebraic geometry, such as the category of schemes and Iwasawa theory, and other 20th-century techniques which were not available to Fermat.

Please , to discuss your proof , please let us first now some thing about the techniques used in your work. And why you think it is elementary?

Dear Sir,

Thank you for the details. I have used the technique of creating two equivalent equations to each of the equations

x^3+ y^3==z^3

and

r^p+s^p = t^3

The first equation was proved already by Euler and others for n =3

Therefore without loss of generality , both x and y are considered as non-zero integers, hence z^3=will be non-zero integers , but both z and z^2 irrational. Nothing to prove anything in this equation, and it has been combined with the second equation, for getting a proof in the second equation. The important thing is , my creating equivalent equations to each of the two equations, using the parameters called a, b,c,d,e and f

In the above two equivalent equations ,I have Incorporated one Euler's equation

2^n =7.k^ 2+l^2

I am finding out the values for a,b,c,dear and f as well as the equivalent values of 2^n, 7.k^2 and l^2

and then I am putting these equivalent values in the Euler's equation . We get a different equation called equation (B). On finding out the rational terms on both sides of Equation (B), and simplifying , I get the result rst=0

Initially we had hypothesized that all r,s and t are non-zero integers, and we have proved the theorem by method of contradiction.

I cannot compare my original proof , which though elementary, was only possible after my trying with thousands of equivalents, and got failure in all the earlier attempts, since every time I got the rational terms only getting cancelled on both sides of Equation (B)

It is impossible to compare my proof with that of Prof. Sir Andrew Wiles, whose proof on Shimura-Taniyama Taniyama Conjecture , is something different.

However , I find slight similarity with that proof with mine: There Frey thought of an Elliptic Curve

y^2=x(x-a^p) (x+b^p)

where he interpolated the Fetmat's equation

a^p+b^p= c^p.

Similarly I had interpolated the Euler's equation into the two equivalent equations of Fermat's.

If you ask me why Euler's equation ,and not any other equation like Pell's equation ,etc. my only answer will be using the Euler's equation I was able to achieve a success in getting the result rst=0.

Please read it as t^p, and not t^3.

Here p is any prime >3.

I don't think that there are anything wrong in taking together two Fetmat's equations ,one for the index 3, and the other for index =p ,any prime >3, inasmuch I maintain z and z^2 irrational, x,y, z^3 non-zero integers .And in the other Fetmat's equation I have not put any restrictions on all possible values of r,s and t, as non-zero integers, and finally proving that only a trivial solution exists in the second equation with either r=0, or s=0, or t=0.

I believe my methodology and logic , and computation of rational terms fit into mathematics

Coming back to the question of Prof.Maged " why I think it is elementary", I just quote from Wikhipedia : In Mathematics , an elementary proof is a proof that only used basic techniques. More specifically , the term is used in number theory to refer to proofs that make no use of complex analyy; a proof which can be accomplished using only real numbers ( that is, real Analysis instead of Complex Analysis). Lol

Creating two equivalent equations ,to the two Fermats equations and from them to create another new equation called equation (B),and getting the result rst =0, was not an easy task for me. I tried thousands of such equivalent equations for many years, and on every attempt the rational terms on both sides of Equation (B) , only got cancelled out on both sides without yielding any result .But I believed that the equation (B ), at some point time ,should tilt at some point of time to give room for the proof, because there was a theorem waiting there !

The PDF file of the published paper is attached to this message.

P.N.Seetharaman.

OK P.N.Seetharaman Seetharaman

I invite valuable comments on my published paper ( enclosed herewith) from number theorists.

As a Mathematics graduate student this is exciting news (if the proof is verified by peers) because it gives us a chance to understand the proof to a result that has stumped so many brilliant mathematicians in the past.

I would earnestly request you to kindly go through my paper, very carefully, and ascertain yourself that everything is correct. Here you are the Referee yourself! You have a sharp pencil and tick item , bit by bit

You may also kindly listen to my six minutes talk in YouTube by typing :

P.N. Seetharaman : An elementary proof for Fermat's Last Theorem.

It took me sisteen years of continuous work to get this proof .

I'm afraid I am very busy at the moment with my studies at Oxford (am in the 6th week of Hilary term) but I've saved the pdf to look at over the Easter holidays in 2 weeks time and I can certainly spare 6 minutes to listen to your Youtube video.

I am amazed at the level of commitment and hard work that has gone behind this work so for that I applaud you!