Number Theory

   

Infinitely Many Solutions of Wide Class of Diophantine Equations

Authors: Zbigniew Płotnicki


This article contains my Diophantine equations solutions. I am presenting this mathematical work mainly to attract attention to my proof that special relativity is false that you can find on vixra.org under title “Proof that special relativity is false”.

I am presenting this mathematical work mainly to attract attention to my proof that special relativity is false.

I have worked on diophantine solutions for more than two years. I can prove that my work is completely independent from the work of others and that two years ago I had solution to (as I call it) general case for solutions without little Fermat theorem and simple case with little Fermat theorem, which is much more than others achieved, but I didn’t want to publish it until it would be complete. I sent it to the Polish profesors of mathematics and to myself so I really can prove and document that I had it two years ago. I sent it for example on 10/26/2011 to polish full professor PhD. Edmund Puczylowski from Univeristy of Warsaw and I can prove it with my correspondence with him (I gave full content of this document that I sent to him in Appendix 1). I sent also some diophantine solutions (the simplest case with use of little Fermat theorem) to full professor PhD. Jerzy Tiuryn from Univeristy of Warsaw on 02/23/2011 and I can prove it too.

I’ve searched the Internet and found very little work on this matter:
Wolfram – nothing.
Wikipedia: Fermat Last Theorem/Diophantine equations – single special case;
http://cp4space.files.wordpress.com/2012/10/moda-ch12.pdf – that does not define all solutions

But what I’ve seen is that:
There is given really very little solutions in comparison to my solutions,
There are not all solutions of (as I call it) “general” or at least “simple” case of presented equations for the cases like for example: ua^x+wb^y=vc^z
There is not proof that presented solutions are all such (wich I call “complex not derived”) solutions for any case, like for example: ua^x+wb^y=vc^z,
There is not proof when there exist such (complex not derived) solutions,
There are not solutions for simultaneous equations
There are not solutions for rational exponents
As I know work of others contains only case of solution when SUM_(i=1..n)(c_i/d*a_i^(x_i))=b^z=(SUM_(i=1..n)(c_i/d*l_i^(x_i))^(t*lcm(x)+1) or even only SUM_(i=1..n)(a_i^(x_i))=b^z=(SUM_(i=1..n)(l_i^(x_i)))^(t*lcm(x)+1) which is very little. And does not show how to solve equation without solving qz=t*lcm(x)+1, so this algorithm to solve equation has not complexity O(1) while my has O(1).
There is no solution given for any case (especially for general case) to equations that has coefficient not equal to 1 on the right side.

Which all and much more I’ve done in this article.

If my Diophantine equation solutions are not enough I also give a inverse function to Li(n) function. I think it should be enough.

I named this kind of Diophantine equation that I’ve described in this article after my surname, because I need to refere to them in this article.

Finally I can present part of my work. Thanks for reading. I have more and I will publish it in my book that should come out next year.

Please, give me an endorsement on arxiv (on physics, math), if you can. My username on arxiv is at the end of abstract in the document.
(and let me know at my e-mail address which is at first page of the document)

Comments: 71 Pages.

Download: PDF

Submission history

[v1] 2013-07-16 18:08:48

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