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#151 2014-06-03 23:19:44

individ
Member
Registered: 2014-03-16
Posts: 171

Re: Formulas for the solution of Diophantine equations.

Equation:

Has the solution:

- Any integers.

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#152 2014-06-06 20:40:22

individ
Member
Registered: 2014-03-16
Posts: 171

Re: Formulas for the solution of Diophantine equations.

Equation: 

Has the solution:

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#153 2014-06-10 01:16:51

individ
Member
Registered: 2014-03-16
Posts: 171

Re: Formulas for the solution of Diophantine equations.

Solutions of the equation:

you can record if the root of the whole:

Then using the solutions of the equation Pell:

Then the formula of the solution, you can write:

If the root is a need to find out if this is equivalent to the quadratic form in which the root of the whole. This is usually accomplished this replacement:

in such number

Forgot to say. The characters inside the brackets do not depend on the sign of the Pell equation. It depends only before

Last edited by individ (2014-06-10 01:22:32)

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#154 2014-06-12 02:53:18

individ
Member
Registered: 2014-03-16
Posts: 171

Re: Formulas for the solution of Diophantine equations.

For the equation:

The solution can be written using the factorization, as follows.

Then the solutions have the form:

I usually choose the number

such that the difference:
was equal to:

Although your desire you can choose other.

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#155 2014-06-12 03:28:02

individ
Member
Registered: 2014-03-16
Posts: 171

Re: Formulas for the solution of Diophantine equations.

It was necessary to write the solution in a more General form:

- integers.

Decomposing on the factors as follows:

The solutions have the form:

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#156 2014-06-12 06:03:30

individ
Member
Registered: 2014-03-16
Posts: 171

Re: Formulas for the solution of Diophantine equations.

I hope it is clear that I am for the challenge?
See you there: http://en.wikipedia.org/wiki/Erdős–Straus_conjecture

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#157 2014-06-12 16:54:42

individ
Member
Registered: 2014-03-16
Posts: 171

Re: Formulas for the solution of Diophantine equations.

For the equation:


You can write a little differently. If unfold like this:

The solutions have the form:

Similarly for the other equations can be written.

Decomposing on the factors as follows:

The solutions have the form:

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#158 2014-06-19 18:39:06

individ
Member
Registered: 2014-03-16
Posts: 171

Re: Formulas for the solution of Diophantine equations.

For the equation:

The solutions have the form:

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#159 2014-06-24 18:43:03

individ
Member
Registered: 2014-03-16
Posts: 171

Re: Formulas for the solution of Diophantine equations.

Nowhere formula fails to print.
So was forced to print there.  http://vixra.org/abs/1406.0114
And there:   http://vixra.org/abs/1406.0147

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#160 2014-06-24 23:02:52

individ
Member
Registered: 2014-03-16
Posts: 171

Re: Formulas for the solution of Diophantine equations.

The formula looks quite cumbersome, but it has simplified and will write here is simple.

Equation:

Has the solution:

- any integers, any sign.

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#161 2014-06-29 20:26:03

individ
Member
Registered: 2014-03-16
Posts: 171

Re: Formulas for the solution of Diophantine equations.

Equation:

Formula of the solution, you can write:

- integers of any sign.

After substitution and obtain numerical results. It should be divided into common divisor. To get a primitive solution.

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#162 2014-07-02 23:49:52

individ
Member
Registered: 2014-03-16
Posts: 171

Re: Formulas for the solution of Diophantine equations.

Quite simply turned out to solve this Diophantine equation, when he made the assumption that the solutions of these equations symmetric.

So given this equation:

And symmetric solution is quite simple written.

- integers of any sign.

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#163 2014-07-03 21:38:20

individ
Member
Registered: 2014-03-16
Posts: 171

Re: Formulas for the solution of Diophantine equations.

In General, for any equation like this:

Symmetric solution can be written:

- integers, any sign.

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#164 2014-07-06 19:47:12

individ
Member
Registered: 2014-03-16
Posts: 171

Re: Formulas for the solution of Diophantine equations.

Can be infinitely many of polynomials of second degree which would define all integers of any .

Looks like that and actually have to solve this Diophantine equation.

If the number 

- any whole and given us.

Then this number can be found the solution of the equation as:

- the number of different parity.
It was easier to solve the inverse problem. And polynomial has turned out as a solution of the equation.

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#165 2014-07-06 20:17:06

individ
Member
Registered: 2014-03-16
Posts: 171

Re: Formulas for the solution of Diophantine equations.

I'm with these people are surprised! Wanted to find a polynomial - I've found, but they are still not satisfied.

http://mathoverflow.net/questions/9731/ … 491#173491

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#166 2014-07-07 03:59:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,376

Re: Formulas for the solution of Diophantine equations.

Satisfied with what?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#167 2014-07-07 04:32:00

individ
Member
Registered: 2014-03-16
Posts: 171

Re: Formulas for the solution of Diophantine equations.

These idiots want to find a polynomial with two parameters and the degree greater than 2 . Which would describe all integers. I showed them and say that there is only of degree 2.

And they were all erased and looking for what does not exist. As these fools to explain don't know.

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#168 2014-07-07 04:42:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,376

Re: Formulas for the solution of Diophantine equations.

Calling them idiots is not going to get them to like you.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#169 2014-07-07 04:48:55

individ
Member
Registered: 2014-03-16
Posts: 171

Re: Formulas for the solution of Diophantine equations.

Well then let looking for this polynomial. But why my formula to erase?

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#170 2014-07-07 04:49:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,376

Re: Formulas for the solution of Diophantine equations.

What did you post with the formula?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#171 2014-07-07 04:54:00

individ
Member
Registered: 2014-03-16
Posts: 171

Re: Formulas for the solution of Diophantine equations.

The formula that had written and they wiped. They are all my formula wash. Do not like very formula.

't understand that there is no polynomial of degree greater than 2.  Which would define all integers. Depending on two parameters.

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#172 2014-07-07 04:54:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,376

Re: Formulas for the solution of Diophantine equations.

Did you call them idiots when you posted your formula?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#173 2014-07-07 04:55:54

individ
Member
Registered: 2014-03-16
Posts: 171

Re: Formulas for the solution of Diophantine equations.

I don't understand what you are saying. Write simpler.

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#174 2014-07-07 04:58:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,376

Re: Formulas for the solution of Diophantine equations.

You say you only posted a formula and they deleted it?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#175 2014-07-07 04:59:52

individ
Member
Registered: 2014-03-16
Posts: 171

Re: Formulas for the solution of Diophantine equations.

Yes erased! They always my formula wash.

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