<![CDATA[Math Is Fun Forum / Formulas for the solution of Diophantine equations.]]> 2019-07-11T10:36:23Z FluxBB http://www.mathisfunforum.com/viewtopic.php?id=20642 <![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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http://www.mathisfunforum.com/profile.php?id=204469 2019-07-11T10:36:23Z http://www.mathisfunforum.com/viewtopic.php?pid=410009#p410009
<![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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http://www.mathisfunforum.com/profile.php?id=204469 2019-07-03T12:20:28Z http://www.mathisfunforum.com/viewtopic.php?pid=409907#p409907
<![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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http://www.mathisfunforum.com/profile.php?id=204469 2019-06-23T13:26:44Z http://www.mathisfunforum.com/viewtopic.php?pid=409752#p409752
<![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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http://www.mathisfunforum.com/profile.php?id=204469 2019-05-05T09:27:51Z http://www.mathisfunforum.com/viewtopic.php?pid=408351#p408351
<![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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http://www.mathisfunforum.com/profile.php?id=204469 2018-07-26T12:27:30Z http://www.mathisfunforum.com/viewtopic.php?pid=404951#p404951
<![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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http://www.mathisfunforum.com/profile.php?id=204469 2018-06-08T16:49:25Z http://www.mathisfunforum.com/viewtopic.php?pid=404125#p404125
<![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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http://www.mathisfunforum.com/profile.php?id=204469 2018-05-01T08:39:03Z http://www.mathisfunforum.com/viewtopic.php?pid=403385#p403385
<![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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http://www.mathisfunforum.com/profile.php?id=204469 2018-01-08T05:35:17Z http://www.mathisfunforum.com/viewtopic.php?pid=401712#p401712
<![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:

- any integer asked us.

A similar method can be used for other type of equations.

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http://www.mathisfunforum.com/profile.php?id=204469 2017-12-16T05:14:01Z http://www.mathisfunforum.com/viewtopic.php?pid=401510#p401510
<![CDATA[Re: Formulas for the solution of Diophantine equations.]]> https://math.stackexchange.com/question … 98#2507298

For the equation.

The solution can be written directly.

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http://www.mathisfunforum.com/profile.php?id=204469 2017-11-06T10:14:52Z http://www.mathisfunforum.com/viewtopic.php?pid=401150#p401150
<![CDATA[Re: Formulas for the solution of Diophantine equations.]]> https://math.stackexchange.com/question … 2-d2abx-s2

For the system of equations.

Make such a change.

The solution can be written as.

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http://www.mathisfunforum.com/profile.php?id=204469 2017-10-03T09:25:36Z http://www.mathisfunforum.com/viewtopic.php?pid=400867#p400867
<![CDATA[Re: Formulas for the solution of Diophantine equations.]]> 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
;

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http://www.mathisfunforum.com/profile.php?id=204469 2017-09-19T08:59:29Z http://www.mathisfunforum.com/viewtopic.php?pid=400780#p400780
<![CDATA[Re: Formulas for the solution of Diophantine equations.]]> https://math.stackexchange.com/question … 54#2430154

Solution we write.

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

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