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#201 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-08-06 03:08:25

Equation:

You can write a simple solution:

- any integer asked us.

#202 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-08-04 22:03:33

Then this equation. If there is a solution - they are infinitely many.

Finding solutions-it factor.  To factor. 

We use the solutions of the equation Pell.   

Then the solutions are.

#203 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-08-01 22:56:43

You can write another solution. This is equivalent to the equation:

The solutions have the form:

................................................

..............................................

Will make a replacement.

The solution has the form:

#204 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-08-01 20:25:58

One said that this equation has no solutions. Because the equation Farm has no solutions. It turned out that the solution of this equation is.

Fermat's theorem cannot be proved, if you do not know how to solve Diophantine equations.

This approach cannot be used. This equation has a solution.

The solutions have the form:

- any integer.

#205 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-07-30 00:38:17

In General formula generic for Pythagorean triples looks a little different.

If the number can be represented as a sum of squares. 

The solution has the form:

#206 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-07-29 22:42:51

Perhaps you should write a more General solution of the equation.

If you ask any integers:

- and use the solutions of the equation Pell.

The solution, you can write:

You can write a simple solution without the Pell equation.

If:

If:

#207 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-07-28 17:20:44

To attract attention, it is necessary to solve such a simple equation. 

You could take the equation; 

 

And see the look of his decision. 

 

 

 

 

 

 

 

 

 

- integers of any sign.

If you ask what number it is.

  In the equation.

Decompose the multiplier number and select the number so that solved the linear system of equations.

Then decisions can be recorded.

#208 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-07-24 02:37:41

I think it is better to rewrite the solution for the more General case.

The decision will write it down.

- integer of any sign.
- select no fraction.

It is possible differently.  Choose any number "

"   and the expression lay at the multipliers.

Then the solution can be written.

If you choose "

" - the numbers so that they were not Pythagorean triples. 

We use the solutions of the equation Pell. 

Decisions will write it down.

#209 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-07-22 01:24:39

If you told me to find for a given set.

- integer of any sign.

Then for the equation. 

using factorization. In the following manner.

Then the solutions are.

#210 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-07-21 21:09:15

For the equation:

You can simply write symmetric solutions.

- integers asked us and any sign.

#211 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-07-20 18:42:09

Though it is necessary to write a more General solution of the equation.

The formula looks like this:

..........................................

For our case, the number

- different parity.

#212 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-07-20 17:33:17

Solutions of the equation:

you can easily write:

When

- odd. Formula gives an odd decision. 
The task is certainly simple, but I had to find a formula which would give an odd decision.

#213 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-07-19 23:09:13

Equation:

Has another solution.

- integer of any sign.

#214 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-07-18 18:03:51

The system of equations:

- the number of whole and of any sign.

To make it easier to write the formula will make a replacement.

Then the solution can be written, and they look like.

#215 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-07-16 21:29:33

For the equation: 

The solution, you can write.

- what some integer.

Then using the solutions of the equation Pell. 

The solutions have the form:

- it is necessary to choose such that decisions were intact.

#216 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-07-15 04:38:02

The system of equations:

the solutions have the form:

- integers.

Interesting. These formulas or not describe all solutions?

#218 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-07-13 16:39:35

Didn't understand. This is what? The link does not work.

#219 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-07-08 05:42:17

Yes of course! There is always a chance that someone will understand the method of calculation.
Especially when I wrote this number of solutions.  But even if the method is someone guesses correctly. There will always be a question. Can I solve the equations on another.

These formulas are no longer published, and I only got the opportunity to promote this method.
Some formulas are needed. If someone can - print.

#220 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-07-08 02:41:13

The value of the method of calculation is much greater than the threat delete the message.

#221 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-07-08 02:11:53

There were not asked.   Immediately deleted.
I do not see sense to tell everything.
First, it is necessary that more people learned.

#222 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-07-08 02:01:04

What evidence? They can't equation to solve.
Evidence is too early to say. Many issues are and should be solved before that or to prove.

#223 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-07-07 23:50:50

The simple sense.
Opponents argue that there is no possibility to solve Diophantine equations.
I say that there are some equations which can be solved. And the argument here is the formula of the solution.
And they say that all the same it is impossible to solve all formulas are removed.
And in that way and there is a conversation. I write formulas they are washed.

#224 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-07-07 18:11:34

There asked a similar question in this thread.
http://mathoverflow.net/questions/17354 … 565#173565
I there a few formulas drew. Look how long it will take to remove them.

#225 Re: This is Cool » Formulas for the solution of Diophantine equations. » 2014-07-07 05:56:42

I mean You did not. Okay. Nothing. Look how long they were going to swear.

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