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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,668

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.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**individ****Member**- Registered: 2014-03-16
- Posts: 223

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.

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individ wrote:

There's nothing I can not do.

**Statement**The 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.

'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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,668

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.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**individ****Member**- Registered: 2014-03-16
- Posts: 223

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,668

I know what you or rather google meant.

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

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**individ****Member**- Registered: 2014-03-16
- Posts: 223

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?

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**individ****Member**- Registered: 2014-03-16
- Posts: 223

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.

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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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,668

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.**

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**individ****Member**- Registered: 2014-03-16
- Posts: 223

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/738446/solutions-to-ax2-by2-cz2

*Last edited by individ (2014-04-05 16:44:34)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,668

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.**

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**individ****Member**- Registered: 2014-03-16
- Posts: 223

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,668

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.**

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**individ****Member**- Registered: 2014-03-16
- Posts: 223

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.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,668

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.**

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**individ****Member**- Registered: 2014-03-16
- Posts: 223

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

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**individ****Member**- Registered: 2014-03-16
- Posts: 223

For a private quadratic form:

Using solutions of Pell's equation:

Solutions can be expressed through them is quite simple.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,668

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.**

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**individ****Member**- Registered: 2014-03-16
- Posts: 223

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.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,668

Sorry, I am not following any of that.

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

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**individ****Member**- Registered: 2014-03-16
- Posts: 223

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.

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**individ****Member**- Registered: 2014-03-16
- Posts: 223

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?

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**individ****Member**- Registered: 2014-03-16
- Posts: 223

Diophantine equation:

Has a solution:

more:

- integers asked us.Offline