You are not logged in.
If we consider the Diophantine equation:
If the root is a :
We use the solutions of Pell's equation:
Solutions can be written:
- any integer number given by usnumber:
- are solutions of the following equationsIf we take the solutions of Pell's equation:
number
- are solutions of the equation:wherein:
number
- solutions of the equation:These formulas allow us to find some solutions of Pell's equation using solutions of simpler equations. At least there will be another opportunity to find a solution to this equation.
Later draw solutions with other factors.
For Diophantine equations:
Symmetric solutions can be written as:
Solutions have the form:
Solutions have the form:
Solutions have the form:
Solutions have the form:
- what some integers.I knew it. Asked for another task.
Clear! With as waterboy? It is possible to find the problem?
I do not understand the question.
Problems there? What is it?
In the equation:
If the ratio is such that the root of an integer:
Then the solution is:
...........................................................................................................................................................
............................................................................................................................................................
And more.
.............................................................................................................................................................
.............................................................................................................................................................
Any. Something does not work? The task of the yoke there is a promotion?
system:
Solution has the form:
The traveling salesman problem a special case.
The task is similar, only the points necessary to deliver various goods.
Formulation of the problem is needed.
I need to check out one algorithm. While like running, but I would like to solve the problem when someone gives independent condition.
This system of equations solved before Diophantus.
Although elementary obtained such solutions:
more:
more:
more:
But these solutions are not of interest. The fact that a decision that leads Diophantus described sleduyushy formula.
I do not think that Diophantus accidentally brought this decision. But then he had to know this formula. Although the cause could not be more simple. And specifically chose not even solution.
Well you can and draw another formula.
The most interesting thing there is that the formula that led, like should not give mutually simple solutions, but after sokrasheniya on common divisor can be obtained and are relatively prime solutions. This means that the formula itself describes as relatively prime so no. Coprime solutions - there are private solutions.
bobbym - there is such a problem waterboy. It is more common than the traveling salesman problem.
The idea that there is a water-carrier and donkey with him, he goes round the points of a certain amount of water. At each point, it delivers a certain amount of water. Load on the donkey is calculated as the product of distance traveled by the mass transferred in passing this way. Naturally we must honor the weight of the donkey.
The challenge is to find the optimal algorithm allows waterboy make the best route to load the donkey was minimal. The algorithm is, but there is a need to test it.
You must specify on the plane, so it was easier to believe in the whole coordinate delivery points and the amount of cargo there.
Points can take 50 pieces
I find the algorithm route, and my opponents will look better.
Just when I choose my location I say pick a specific location. So I need not dependent task.
system of equations:
Solutions and can be written as follows.
And more:
- are integers and can be any mark.
I know. About what I said, but do not take my stuff there and no one would publish. If you have the opportunity to do.
Did not understand what a sponsor? Book to buy?
If you have the opportunity to publish these formulas. I think this is the best that can be done
I can not. I can not really anywhere.
I stir in the forums. In arhiv.org there can not permit necessary.
All the equations of course can not be solved. But there are groups of equations which are amenable to solutions. You can certainly say that the equation can not be solved and throw this thing. But you can try to figure out what can be solved for them and come up with methods of solution.
Yes, I know! So my article and do not print there. They have with me can not argue - no arguments. So I either ignore or erase.
These formulas only got me. The fact - as shown, the problem that the Hilbert 10 has a negative solution. That is not on the coefficients of the equation a formula that said that the solution y of the equation is or not. But it turns out that such formulas exist.
First want to print solution Legendre's equation in a general form, and other systems of equations. All formulas are silent - to show that the equation can be solved in general form. Well, then he is the method of calculation.
Everything is much more banal. A lot of effort spent on it, and do not give me the opportunity to even publish an article.
The method is not published. I can not talk about it.
In Diophantine equations often can write infinitely many formulas describing their solutions. And with an entirely different formula may describe the same solutions. So what's the problem? Do not like it that a lot of decisions?
Using the initial solutions and some geometric formulas Diophantine solutions were obtained. I know a few, but I'm not going to not draw their formulas? I thought that his method in the more general case and got his formula.
I said that I do not have this book so I can not judge his formulas.
If these formulas you do not like - time for you to find others. But when solving the equations do not always come short. And it's not my fault - the equations themselves decide what they need to have a formula.