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**individ****Member**- Registered: 2014-03-16
- Posts: 329

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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**individ****Member**- Registered: 2014-03-16
- Posts: 329

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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**individ****Member**- Registered: 2014-03-16
- Posts: 329

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.

*Last edited by individ (2019-07-03 00:21:35)*

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**individ****Member**- Registered: 2014-03-16
- Posts: 329

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...*Last edited by individ (2019-07-11 16:28:48)*

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**individ****Member**- Registered: 2014-03-16
- Posts: 329

https://math.stackexchange.com/question … s-part-two

*Last edited by individ (2019-09-14 19:35:05)*

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**individ****Member**- Registered: 2014-03-16
- Posts: 329

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**individ****Member**- Registered: 2014-03-16
- Posts: 329

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**individ****Member**- Registered: 2014-03-16
- Posts: 329

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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**individ****Member**- Registered: 2014-03-16
- Posts: 329

https://math.stackexchange.com/question … 72#4370472

There are various variants of such equations. For example like this.

https://artofproblemsolving.com/communi … _variables

When solving such equations.

Pythagorean triples can help us. Take any two Pythagorean triples.

Then the solutions can be written in this form. Then the truth needs to be reduced by a common divisor.

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