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https://math.stackexchange.com/question … 2-d2abx-s2

For the system of equations.

Make such a change.

The solution can be written as.

https://math.stackexchange.com/question … 78#2435778

For the equation.

All variations of the same formula. As the number of solutions of course need to consider all possible factorization. Too much ends quickly. The number must be greater than 1.

Consider this example.

;Let

Means ; ;https://math.stackexchange.com/question … 54#2430154

Solution we write.

https://mathoverflow.net/questions/2793 … 390#279390

A better equation to solve in General.

As already mentioned, the task is reduced to some equivalent to the Pell equation. Actually reduced to this form.

Solution we write.

Or so.

https://math.stackexchange.com/question … uch-xyz22x

For the equation.

It is possible to reduce the parameterization of the solutions to some equivalent to the Pell equation.

It has the form.

These parameters can be recorded through the solution of the equation Pell.

https://mathoverflow.net/questions/2777 … -variables

Rewrite the system of equations.

The solution of this system can be written as.

https://mathoverflow.net/questions/2647 … 193#275193

There is one idea. To search for the solution of the equation.

If we know any solution

of this equation. Then it is possible to find another . Make such a change.Then the following solution can be found by the formula.

https://math.stackexchange.com/question … 18#2343918

Better system to write this.

For simplicity, the formula is written. Solution write using other parameters which will be determined next.

Express these options through the following polynomial.

Express these options through the following polynomial.

And now Express them via the parameters set by us

.The formula is very cumbersome and I wasn't able to test it. We must believe not made any mistake?

More simple parameterizations.

https://math.stackexchange.com/question … m3n3-holds

For the equation.

We use the solutions of the equation Pell.

Then the solution can write.

And again.

All the numbers can have any sign.

NakulG wrote:

Hi can you suggest a good charting software, i am trying to plot conic section, intersection of cylindrical cones and a plane. If you can suggest a good charting software that would be great. I tried Asymptote and geogebra... not working out for me.

thanks

Do not write the question here! If you need to open a separate topic. There can be about a specific equation to tell.

I solve the equation. Programs do not write.

Build a curve at the intersection of two surfaces of a standard task. What is the program?

If you need to find the integral points. Formulate problem as a system of nonlinear equations. Then it will try to solve it.

https://math.stackexchange.com/question … 01#2280801

Spread by multipliers...

Decisions can be recorded.

https://math.stackexchange.com/question … x2y2-z2w21

Write solutions like this.

https://math.stackexchange.com/question … e-equation

For the solution of the equation.

Solution we write expanding on the multipliers.

And ;http://math.stackexchange.com/questions … 24#2214424

For the solution of the equation.

You must use the solutions of the equation.

You can use solutions which are recorded in the subject. http://math.stackexchange.com/questions … 219#709219

Then using the solutions of this equation can be substituted into the formula and find us.

http://math.stackexchange.com/questions … te-integer

For the equation.

You can write such a parameterization.

http://math.stackexchange.com/questions … rfect-squa

For odd numbers.

Decompose the number into factors.

The solution can be written as.

It is seen that for all odd numbers are infinitely many solutions, not just

.http://mathoverflow.net/questions/26315 … e-integers

Representation of a number we write.

I think that the only way to record the desired polynomial is to use the solutions of any equation.

Knowing the solutions of this equation and substituting them into the linear Diophantine equation.

variables which are solutions of this equation. Then the solution of the first equation can be written as.https://www.artofproblemsolving.com/com … umthory_13

Knowing one solution, others will find the formula.

Decisions will be.

http://math.stackexchange.com/questions … 09#2129909

For the system of equations.

Lay on multipliers.

Solutions written in this form. Any whole number. It is seen that solutions in integers there is not only for but for any other integer.This formula will be better ....

Decompose the number $T$ in two different ways.

http://math.stackexchange.com/questions … c-acb-sqrt

Solve the system.

The solution can be written as.

http://math.stackexchange.com/questions … m21-and-m1

To solve this system of equations - it is necessary to solve the system.

It is necessary to find a parameterization to figurirovallo Pell. It is possible for example to record this.

We need a case of when.

Knowing the first decision

The rest can be found by the formula.

Although this equation can be not enough. We need to find when there are multiple solutions.

http://mymathforum.com/number-theory/33 … -bz-c.html

For Diophantine equation

If the root is integer.

We use the solutions of the equation Pell.

The solution then can be written in this form.

To find all solutions is necessary to solve the more General equation. With different coefficients.

http://math.stackexchange.com/questions … 30#2077030

You can record a similar system.

Parametrization of solutions we write this.

Consider a special case.

Using the solutions of the equation Pell.

Enough to know first, everything else will find a formula.

The solution then write.

These solutions are negative.

And a positive decision of the same are determined by the Pell equation.

Use the first solution.

Next find the formula.

Will make a replacement.

The decision record.