<![CDATA[Math Is Fun Forum / Formulas for the solution of Diophantine equations.]]> 2021-02-25T08:43:49Z FluxBB https://www.mathisfunforum.com/viewtopic.php?id=20642 <![CDATA[Re: Formulas for the solution of Diophantine equations.]]> https://math.stackexchange.com/question … 86#4039186

To solve the Diophantine equation.

It is necessary to use the solution of the following equation.

There are solutions when the coefficient can be represented as the sum of squares.

And the solution itself can be presented in this form.

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<![CDATA[Re: Formulas for the solution of Diophantine equations.]]> https://mathoverflow.net/questions/8835 … 028#369028

https://arxiv.org/abs/2008.04440

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<![CDATA[Re: Formulas for the solution of Diophantine equations.]]> https://math.stackexchange.com/question … e-equation

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<![CDATA[Re: Formulas for the solution of Diophantine equations.]]> https://math.stackexchange.com/question … s-part-two

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<![CDATA[Re: Formulas for the solution of Diophantine equations.]]> A link to the discussion of the equation....

https://dxdy.ru/topic134512.html

I kind of wrote 5 parametric solution.

For the case when

or
.... get the formula for 4 cubes...

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<![CDATA[Re: Formulas for the solution of Diophantine equations.]]> https://math.stackexchange.com/question … y2-a2ab-b2

Solution of equation.

Can be written using solutions to the Pell equation....

Knowing the first solutions for....

The following can be found by the formula.

Will make a replacement for the simplified entry....

And then the solutions of the equation can be written in the form...

So the Pell equation has infinitely many solutions, it means for any number
- solutions will always be and infinitely many.

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<![CDATA[Re: Formulas for the solution of Diophantine equations.]]> https://mathoverflow.net/questions/3343 … 624#334624

To solve the Diophantine equation.  Where

is any given number...

Solutions can be expressed through the following solutions to the Pell equation.

And then the decisions can be recorded...

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<![CDATA[Re: Formulas for the solution of Diophantine equations.]]> https://math.stackexchange.com/question … 71#3214271

Use another equation.

And we use solutions to the Pell equation.

any number.

Decisions then write down so.

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<![CDATA[Re: Formulas for the solution of Diophantine equations.]]> https://math.stackexchange.com/question … l2-in-inte

You can record such a parameterization of solutions.

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<![CDATA[Re: Formulas for the solution of Diophantine equations.]]> https://math.stackexchange.com/question … -b-i-3-and

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<![CDATA[Re: Formulas for the solution of Diophantine equations.]]> http://math.hashcode.ru/questions/15654 … 576#156576

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<![CDATA[Re: Formulas for the solution of Diophantine equations.]]> https://math.stackexchange.com/question … 1-y2y1n2n1

To solve the Diophantine equation.

It is necessary to use the solutions of the Pell equation.

Then the solutions can be written as follows.

For positive you need to take decisions at

.

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<![CDATA[Re: Formulas for the solution of Diophantine equations.]]> https://math.stackexchange.com/question … 64#2596464

The solution of the system of equations can be written in this form.

are any integer.

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<![CDATA[Re: Formulas for the solution of Diophantine equations.]]> https://math.stackexchange.com/question … 03#2568803

For this type of equations - which has something in common...

Record regarding

-  A different equation. And replace solving a system of equations, the solution of the same equation.

We write as....

And instead of solving the system, we solve it.

You can write a simple solution: