Formulas for the solution of Diophantine equations.

individ · 2014-06-03 23:19:44

Equation:

Has the solution:

- Any integers.

individ · 2014-06-06 20:40:22

Equation:

Has the solution:

individ · 2014-06-10 01:16:51

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)

individ · 2014-06-12 02:53:18

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.

individ · 2014-06-12 03:28:02

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

- integers.

Decomposing on the factors as follows:

The solutions have the form:

individ · 2014-06-12 06:03:30

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

individ · 2014-06-12 16:54:42

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:

individ · 2014-06-19 18:39:06

For the equation:

The solutions have the form:

individ · 2014-06-24 18:43:03

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

individ · 2014-06-24 23:02:52

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

Equation:

Has the solution:

- any integers, any sign.

individ · 2014-06-29 20:26:03

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.

individ · 2014-07-02 23:49:52

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.

individ · 2014-07-03 21:38:20

In General, for any equation like this:

Symmetric solution can be written:

- integers, any sign.

individ · 2014-07-06 19:47:12

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.

individ · 2014-07-06 20:17:06

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

bobbym · 2014-07-07 03:59:21

Satisfied with what?

individ · 2014-07-07 04:32:00

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.

bobbym · 2014-07-07 04:42:22

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

individ · 2014-07-07 04:48:55

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

bobbym · 2014-07-07 04:49:57

What did you post with the formula?

individ · 2014-07-07 04:54:00

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.

bobbym · 2014-07-07 04:54:48

Did you call them idiots when you posted your formula?

individ · 2014-07-07 04:55:54

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

bobbym · 2014-07-07 04:58:49

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

individ · 2014-07-07 04:59:52

Yes erased! They always my formula wash.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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

Re: Formulas for the solution of Diophantine equations.

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