Formulas for the solution of Diophantine equations.

ShivamS · 2014-04-23 01:22:26

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

bobbym · 2014-04-23 01:25:28

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

ShivamS · 2014-04-23 01:31:52

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)

bobbym · 2014-04-23 01:49:44

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

individ · 2014-04-24 04:17:53

system of equations:

Solutions and can be written as follows.

And more:

- are integers and can be any mark.

individ · 2014-04-25 20:35:45

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.

individ · 2014-04-25 22:54:59

This system of equations solved before Diophantus.

Although elementary obtained such solutions:

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.

bobbym · 2014-04-26 01:38:10

Hi;

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

individ · 2014-04-26 01:41:35

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

bobbym · 2014-04-26 02:00:31

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

individ · 2014-04-26 02:15:53

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.

individ · 2014-04-26 22:26:54

system:

Solution has the form:

bobbym · 2014-04-27 05:31:57

Hi;

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

individ · 2014-04-27 05:36:00

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

individ · 2014-04-29 03:33:57

In the equation:

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

Then the solution is:

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

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

And more.

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

bobbym · 2014-04-29 16:00:55

Hi;

The formula in post #106 checks out.

individ · 2014-04-29 16:15:00

I do not understand the question.
Problems there? What is it?

bobbym · 2014-04-29 21:14:40

Hi;

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

individ · 2014-04-29 21:16:47

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

bobbym · 2014-04-29 21:23:10

Hi;

I was saying that I checked your solutions to

they are correct.

individ · 2014-04-29 21:24:53

I knew it. Asked for another task.

bobbym · 2014-04-30 00:11:11

I knew it.

Yes, but now I know it too.

individ · 2014-04-30 23:43:45

For Diophantine equations:

Symmetric solutions can be written as:

Solutions have the form:

- what some integers.

individ · 2014-05-01 02:35:28

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 us

number:

- are solutions of the following equations

If 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.

individ · 2014-05-02 02:29:29

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.

Math Is Fun Forum

#101 2014-04-23 01:22:26

Re: Formulas for the solution of Diophantine equations.

#102 2014-04-23 01:25:28

Re: Formulas for the solution of Diophantine equations.

#103 2014-04-23 01:31:52

Re: Formulas for the solution of Diophantine equations.

#104 2014-04-23 01:49:44

Re: Formulas for the solution of Diophantine equations.

#105 2014-04-24 04:17:53

Re: Formulas for the solution of Diophantine equations.

#106 2014-04-25 20:35:45

Re: Formulas for the solution of Diophantine equations.

#107 2014-04-25 22:54:59

Re: Formulas for the solution of Diophantine equations.

#108 2014-04-26 01:38:10

Re: Formulas for the solution of Diophantine equations.

#109 2014-04-26 01:41:35

Re: Formulas for the solution of Diophantine equations.

#110 2014-04-26 02:00:31

Re: Formulas for the solution of Diophantine equations.

#111 2014-04-26 02:15:53

Re: Formulas for the solution of Diophantine equations.

#112 2014-04-26 22:26:54

Re: Formulas for the solution of Diophantine equations.

#113 2014-04-27 05:31:57

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#114 2014-04-27 05:36:00

Re: Formulas for the solution of Diophantine equations.

#115 2014-04-29 03:33:57

Re: Formulas for the solution of Diophantine equations.

#116 2014-04-29 16:00:55

Re: Formulas for the solution of Diophantine equations.

#117 2014-04-29 16:15:00

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#118 2014-04-29 21:14:40

Re: Formulas for the solution of Diophantine equations.

#119 2014-04-29 21:16:47

Re: Formulas for the solution of Diophantine equations.

#120 2014-04-29 21:23:10

Re: Formulas for the solution of Diophantine equations.

#121 2014-04-29 21:24:53

Re: Formulas for the solution of Diophantine equations.

#122 2014-04-30 00:11:11

Re: Formulas for the solution of Diophantine equations.

#123 2014-04-30 23:43:45

Re: Formulas for the solution of Diophantine equations.

#124 2014-05-01 02:35:28

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#125 2014-05-02 02:29:29

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