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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,640

Why not have it looked over by some professor and then publish it in some journal?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,991

He will have to find one. If you have ever read Dudley's book then you know their disdain for non-professionals.

**In mathematics, you don't understand things. You just get used to them.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,640

I do not think I have, but I know most professors only like working with actual students (which individ could be).

*Last edited by ShivamS (2014-04-23 01:32:21)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,991

He might be but my feeling is that he is a rebel. He has outlined briefly his problems on other forums and blogs.

**In mathematics, you don't understand things. You just get used to them.**

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**individ****Member**- Registered: 2014-03-16
- Posts: 236

system of equations:

Solutions and can be written as follows.

And more:

- are integers and can be any mark.

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**individ****Member**- Registered: 2014-03-16
- Posts: 236

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.

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**individ****Member**- Registered: 2014-03-16
- Posts: 236

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.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,991

Hi;

In post #106, are you saying you think you have a Travelling Salesman algorithm that is new?

**In mathematics, you don't understand things. You just get used to them.**

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**individ****Member**- Registered: 2014-03-16
- Posts: 236

I need to check out one algorithm. While like running, but I would like to solve the problem when someone gives independent condition.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,991

Independent condition? I do not understand. Do you want me to give you a Travelling Salesman problem?

**In mathematics, you don't understand things. You just get used to them.**

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**individ****Member**- Registered: 2014-03-16
- Posts: 236

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.

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**individ****Member**- Registered: 2014-03-16
- Posts: 236

system:

Solution has the form:

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,991

Hi;

For post#106 what are the conditions on a,b and c?

**In mathematics, you don't understand things. You just get used to them.**

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**individ****Member**- Registered: 2014-03-16
- Posts: 236

Any. Something does not work? The task of the yoke there is a promotion?

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**individ****Member**- Registered: 2014-03-16
- Posts: 236

In the equation:

If the ratio is such that the root of an integer:

Then the solution is:

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

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

And more.

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

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,991

Hi;

The formula in post #106 checks out.

**In mathematics, you don't understand things. You just get used to them.**

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**individ****Member**- Registered: 2014-03-16
- Posts: 236

I do not understand the question.

Problems there? What is it?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,991

Hi;

There are no problems, post # 106 is okay. I checked it.

**In mathematics, you don't understand things. You just get used to them.**

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**individ****Member**- Registered: 2014-03-16
- Posts: 236

Clear! With as waterboy? It is possible to find the problem?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,991

Hi;

I was saying that I checked your solutions to

they are correct.

**In mathematics, you don't understand things. You just get used to them.**

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**individ****Member**- Registered: 2014-03-16
- Posts: 236

I knew it. Asked for another task.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,991

I knew it.

Yes, but now I know it too.

**In mathematics, you don't understand things. You just get used to them.**

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**individ****Member**- Registered: 2014-03-16
- Posts: 236

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.Offline

**individ****Member**- Registered: 2014-03-16
- Posts: 236

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.

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**individ****Member**- Registered: 2014-03-16
- Posts: 236

All of numbers can be any character.In Equation:

If the ratio is factored so:

Then we use the solutions of Pell's equation:

where:

Then the solutions are of the form:

All of numbers can be any character.

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