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Equation:
You can write a simple solution:
- any integer asked us.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.
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:
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.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:
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:
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.
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.
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.
For the equation:
You can simply write symmetric solutions.
- integers asked us and any sign.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.Solutions of the equation:
you can easily write:
When
- odd. Formula gives an odd decision.Equation:
Has another solution.
- integer of any sign.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.
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.The system of equations:
the solutions have the form:
- integers.Interesting. These formulas or not describe all solutions?
Sorry. I depicting some problemy were.
Didn't understand. This is what? The link does not work.
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.
The value of the method of calculation is much greater than the threat delete the message.
There were not asked. Immediately deleted.
I do not see sense to tell everything.
First, it is necessary that more people learned.
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.
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.
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.
I mean You did not. Okay. Nothing. Look how long they were going to swear.