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Do you want that on the forum, I spoke about the method of calculation - which was not published anywhere?
I always say that tell me about another method to erase. But the value of the method is much more - than the ability to draw on our formula.
So we'll have to wait.
Who told you that?
I'm still on the method of calculation is not mentioned.
Formulas are obtained by long and beautiful, but the method itself is simple.
In fact, these formulas give the unexpected decision of another famous problem.
It appears there is an algebraic problem where to find a solution much easier than to check the correctness of the decision.
The first time when I was there appeared washed my formula.
I'm trying to prove that my method also has the right to exist, but I can not even publish the formula.
I always say that there is one correct method. This Diophantine geometry and everything that does not fit in it should be erased.
I even invented a method for solving systems of nonlinear algebraic equations. And what is the result? In Russia I was on all the forums is erased or blocked. I can not even on the forums just to paint formula.
I just read on the Russian. Such a book is not seen. My calculation method differs from existing methods.
If method good opportunities - this can be judged by the diversity of equations that decided.
You can see them in my blog. http://www.artofproblemsolving.com/Foru … p?u=206450
That's the difference between my method and from yours. You bust find a solution, and it will build the following solutions.
I decide equation. And get the formula. I search and guessing is not necessary.
Yes this approach I get a broader picture. More clarity.
I have a more interesting formulas are obtained. And there are such formulas on kotryh nobody commemorated.
So what to do? Delete them and forget? Or still think about where they came from?
I get it. Learned that you had in mind. So he just wrote the number, and I am writing formulas. The funny thing is that many people write tsiferki and everyone says - it's good. I write the formula, and I scolded.
Hi! I do not understand what to check? And from whom?
equations
Can be expressed by integers . where the number of characterizes the degree of primitiveness.And more.
If we decide to factor
then:
And the most beautiful solution. If we use the solutions of Pell's equation:
by the way
May appear as a factor in the decision and.If we change the sign :
Then the solutions are of the form:
Another solution of the equation:
- integers asked us.To facilitate the calculations we make the change.
If the ratio is as follows :
If the ratio is as follows:
Then the solutions are of the form:
Then the solutions are of the form:
If the ratio is as follows :
If the ratio is as follows
Then the solutions are of the form :
Then the solutions are of the form :
For the equation:
We can write the solution:
And more:
- integers asked us.When solved this system of equations, it is still the question remains. The following formula describes all written decision or not? Of course you can write a formula in a different form, but it is interesting is not it, but what if there is enough of this formula?
Solutions are defined as integers.
To simplify the notation we make the change :
Then the formula becomes:
If the equation:
We write the solution if the number of:
This can be represented as ideal:Then use the equation Pell:
- integers asked us.Then the solution can be written:
Or again:
It is necessary then to just write another equation:
If we use the solutions of Pell's equation:
formula for the solution can be written, where
integers asked us.And more.
Interestingly, and if you add three triangular numbers, the formula would look like?
For example in the equation:
If we use the solutions of Pell's equation:
Then the solution can be written, where the numbers
whole and sets us.More.
Yes, I know. I was just joking. I wanted to see someone reading my formula or not.
Although equation:
Solutions have the form:
- can be any character.Diophantine equation:
Has a solution:
more:
- integers asked us.In this equation:
- integer number given by the condition of the problem.Generally strange and incomprehensible why a decision as it looks. Who knows what some other solution of this equation?
Though it is necessary to bring the decisions some pretty simple solutions:
the equation:
If the root of the whole:
Then use the solution of Pell's equation:
Solutions can be written:
If a root:
Although it should be mentioned, and the equation:
If the root of the whole:
Using equation Pell:
solutions can be written:And for that decision have to find double formula.
Foreman at all to say?
It's pretty funny! And then after a while to see the professor who found this method?
I understand that my formula will not print one. And advertise method and it will not be anyone's. Nobody would say what he thought.
For a private quadratic form:
Using solutions of Pell's equation:
Solutions can be expressed through them is quite simple.
- can be any character.No, we obtain all the answers. Just them very much interested in the method of calculation. And to prove that we obtain all the solutions we have to show the method of calculation. And this I do not want to do. Do not give me the opportunity to publish these formulas. If someone tell or guess it will not be a priority for me. Now in several Metakhim Silene pytajutsja deciphering these formulas
Think all the same! These formulas do not. Does not exist. And if there is they will say that do not describe all the decisions. And generally explain to forget about these formulas.
Not really want to spoil so many papers on number theory?
Such questions to ask dangerous. May be crazy to call. And I can - I'm used to.
And what's the point? Correct formula tested more than once. They already can safely use.
Such issues are constantly emerging. There's the same. Link does not work I add. Blocked.
Although I poprobyval so. http://math.stackexchange.com/questions … x2-by2-cz2
Since it is necessary to show the use of formulas. Here I give you the answer that gave on another forum the same in connection with the use of these formulas. In fact, this use of formulas from one post. It can be seen that the calculations greatly simplified.
I do not understand! What is the point? Then try to guess the solution to solve the equation on it and build solutions.
Here's an example equation:
Many difficulties in the calculation. What's the point? When substituting into the formula we get solutions immediately.
more:
more:
more:
When numerical coefficients little else can guess the first solution, but when there are large number guessing does not help. Do not we want, but still have to use the formula. And the formula is easier - we immediately obtain the formula for the solution.