Math Is Fun Forum

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Formulas for the solution of Diophantine equations.

Fidelity formulas easily verified.

Hmmm, you keep saying that but as the creator of the idea you should provide those easy derivations. It is not up to me to prove your assertions. You should prove them, they are your ideas and you should know better than I.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

individ

Member

Registered: 2014-03-16

Posts: 339

Re: Formulas for the solution of Diophantine equations.

Here it is not my fault that the formulas are so long. Such they should be. There's nothing I can not do.
While we can be limited by the fact that to know there are formulas for some equations.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Formulas for the solution of Diophantine equations.

There's nothing I can not do.

StatementThe above quote is false.
Proof Assume the contrary.
You either can build a stone that you cannot lift or cannot build a stone like that.
If you cannot build it, we have a contradiction. If you can build it, you cannot lift it, giving rise to a contradiction.

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Formulas for the solution of Diophantine equations.

What we have here is a failure to communicate. He meant there is nothing he can do about it.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Formulas for the solution of Diophantine equations.

I like the omnipotent statement more.

---

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

individ

Member

Registered: 2014-03-16

Posts: 339

Re: Formulas for the solution of Diophantine equations.

If I understand correctly, it is not my fault. Google translates it so. Probably better than the formula used to discuss them.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Formulas for the solution of Diophantine equations.

I know what you or rather google meant.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

individ

Member

Registered: 2014-03-16

Posts: 339

Re: Formulas for the solution of Diophantine equations.

Pretty old problem. Find such pentagonal numbers - which can be represented as a sum of two squares. That is, to prove that such numbers are infinitely many.

So I'm wondering - if I write a formula describing their decision whether it will be sufficient evidence that such numbers are infinitely many?

That is, the following Diophantine equation:

If we use the equation Pell: 

Then using the solutions of this equation can be written solutions of the equation. Sign in and sign Pell alignment of the first alignment should be the same.

more:

Can I assume that the problem was solved? Proved - there are infinitely many pentagonal numbers which can be represented as the sum of two squares?

individ

Member

Registered: 2014-03-16

Posts: 339

Re: Formulas for the solution of Diophantine equations.

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.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Formulas for the solution of Diophantine equations.

Thanks for contributing to our forum.

---

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Formulas for the solution of Diophantine equations.

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

What forum? What post? Please provide a link.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

individ

Member

Registered: 2014-03-16

Posts: 339

Re: Formulas for the solution of Diophantine equations.

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

Last edited by individ (2015-02-15 04:21:40)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Formulas for the solution of Diophantine equations.

Can you write it out as something else that is not a link?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

individ

Member

Registered: 2014-03-16

Posts: 339

Re: Formulas for the solution of Diophantine equations.

And what's the point? Correct formula tested more than once. They already can safely use.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Formulas for the solution of Diophantine equations.

The point is, I would like to see what the number theory guys think.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

individ

Member

Registered: 2014-03-16

Posts: 339

Re: Formulas for the solution of Diophantine equations.

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Formulas for the solution of Diophantine equations.

And if there is they will say that do not describe all the decisions.

If you mean may not generate all the answers they may be right.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

individ

Member

Registered: 2014-03-16

Posts: 339

Re: Formulas for the solution of Diophantine equations.

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

individ

Member

Registered: 2014-03-16

Posts: 339

Re: Formulas for the solution of Diophantine equations.

For a private quadratic form:

Using solutions of Pell's equation: 

Solutions can be expressed through them is quite simple.

- can be any character.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Formulas for the solution of Diophantine equations.

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.

Why do you not want to?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

individ

Member

Registered: 2014-03-16

Posts: 339

Re: Formulas for the solution of Diophantine equations.

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Formulas for the solution of Diophantine equations.

Sorry, I am not following any of that.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

individ

Member

Registered: 2014-03-16

Posts: 339

Re: Formulas for the solution of Diophantine equations.

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:

then the solutions are of the form:

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.

individ

Member

Registered: 2014-03-16

Posts: 339

Re: Formulas for the solution of Diophantine equations.

In this equation:

- integer number given by the condition of the problem.
A rather Tran decision:

- integers asked us.

Generally strange and incomprehensible why a decision as it looks. Who knows what some other solution of this equation?

individ

Member

Registered: 2014-03-16

Posts: 339

Re: Formulas for the solution of Diophantine equations.

Diophantine equation:

Has a solution:

more:

- integers asked us.