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.

]]>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.

]]>For such equations.

Solution write.

]]>It turned out the following. For a square shape

If any number of options

and any coefficients . Solutions is always there.Illustrate 2 coefficients. Similarly solved if the number of different factors. That was evident symmetry and do not get confused is better to take 3 equation.

The solution is easy to write.

Here the representation of 3 options, but it is easy to see that can be written in the form of a combination with any number of options.

]]>For the system of equations.

Solutions can be parameterized.

It is interesting that such triples can be too much. The formula can be increased to any number. That is the same to write not only for 4 partitions, but for any number. The main thing that all the variables were not identical to each other.

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