Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**individ****Member**- Registered: 2014-03-16
- Posts: 276

Equation:

Has the solution:

- Any integers.Offline

**individ****Member**- Registered: 2014-03-16
- Posts: 276

Equation:

Has the solution:

Offline

**individ****Member**- Registered: 2014-03-16
- Posts: 276

Solutions of the equation:

you can record if the root of the whole:

Then using the solutions of the equation Pell:

Then the formula of the solution, you can write:

If the root is a need to find out if this is equivalent to the quadratic form in which the root of the whole. This is usually accomplished this replacement:

in such numberForgot to say. The characters inside the brackets do not depend on the sign of the Pell equation. It depends only before

*Last edited by individ (2014-06-10 01:22:32)*

Offline

**individ****Member**- Registered: 2014-03-16
- Posts: 276

For the equation:

The solution can be written using the factorization, as follows.

Then the solutions have the form:

I usually choose the number

such that the difference: was equal to:Although your desire you can choose other.

Offline

**individ****Member**- Registered: 2014-03-16
- Posts: 276

It was necessary to write the solution in a more General form:

- integers.Decomposing on the factors as follows:

The solutions have the form:

Offline

**individ****Member**- Registered: 2014-03-16
- Posts: 276

I hope it is clear that I am for the challenge?

See you there: http://en.wikipedia.org/wiki/Erdős–Straus_conjecture

Offline

**individ****Member**- Registered: 2014-03-16
- Posts: 276

For the equation:

You can write a little differently. If unfold like this:

The solutions have the form:

Similarly for the other equations can be written.

Decomposing on the factors as follows:

The solutions have the form:

Offline

**individ****Member**- Registered: 2014-03-16
- Posts: 276

For the equation:

The solutions have the form:

Offline

**individ****Member**- Registered: 2014-03-16
- Posts: 276

Nowhere formula fails to print.

So was forced to print there. http://vixra.org/abs/1406.0114

And there: http://vixra.org/abs/1406.0147

Offline

**individ****Member**- Registered: 2014-03-16
- Posts: 276

The formula looks quite cumbersome, but it has simplified and will write here is simple.

Equation:

Has the solution:

- any integers, any sign.Offline

**individ****Member**- Registered: 2014-03-16
- Posts: 276

Equation:

Formula of the solution, you can write:

- integers of any sign.After substitution and obtain numerical results. It should be divided into common divisor. To get a primitive solution.

Offline

**individ****Member**- Registered: 2014-03-16
- Posts: 276

Quite simply turned out to solve this Diophantine equation, when he made the assumption that the solutions of these equations symmetric.

So given this equation:

And symmetric solution is quite simple written.

- integers of any sign.Offline

**individ****Member**- Registered: 2014-03-16
- Posts: 276

In General, for any equation like this:

Symmetric solution can be written:

- integers, any sign.Offline

**individ****Member**- Registered: 2014-03-16
- Posts: 276

Can be infinitely many of polynomials of second degree which would define all integers of any .

Looks like that and actually have to solve this Diophantine equation.

If the number

- any whole and given us.Then this number can be found the solution of the equation as:

- the number of different parity.It was easier to solve the inverse problem. And polynomial has turned out as a solution of the equation.

Offline

**individ****Member**- Registered: 2014-03-16
- Posts: 276

I'm with these people are surprised! Wanted to find a polynomial - I've found, but they are still not satisfied.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,714

Satisfied with what?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

Offline

**individ****Member**- Registered: 2014-03-16
- Posts: 276

These idiots want to find a polynomial with two parameters and the degree greater than 2 . Which would describe all integers. I showed them and say that there is only of degree 2.

And they were all erased and looking for what does not exist. As these fools to explain don't know.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,714

Calling them idiots is not going to get them to like you.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

Offline

**individ****Member**- Registered: 2014-03-16
- Posts: 276

Well then let looking for this polynomial. But why my formula to erase?

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,714

What did you post with the formula?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

Offline

**individ****Member**- Registered: 2014-03-16
- Posts: 276

The formula that had written and they wiped. They are all my formula wash. Do not like very formula.

't understand that there is no polynomial of degree greater than 2. Which would define all integers. Depending on two parameters.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,714

Did you call them idiots when you posted your formula?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

Offline

**individ****Member**- Registered: 2014-03-16
- Posts: 276

I don't understand what you are saying. Write simpler.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,714

You say you only posted a formula and they deleted it?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

Offline

**individ****Member**- Registered: 2014-03-16
- Posts: 276

Yes erased! They always my formula wash.

Offline