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.

]]>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.

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Spread by multipliers...

Decisions can be recorded.

]]>Write solutions like this.

]]>For the solution of the equation.

Solution we write expanding on the multipliers.

And ; ]]>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.

]]>For the equation.

You can write such a parameterization.

]]>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

.]]>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.]]>Knowing one solution, others will find the formula.

Decisions will be.

]]>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.

]]>Solve the system.

The solution can be written as.

]]>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.

]]>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.

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