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#426 2019-05-04 21:27:51

individ
Member
Registered: 2014-03-16
Posts: 323

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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#427 2019-06-23 01:26:44

individ
Member
Registered: 2014-03-16
Posts: 323

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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#428 2019-07-03 00:20:28

individ
Member
Registered: 2014-03-16
Posts: 323

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.

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

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#429 2019-07-10 22:36:23

individ
Member
Registered: 2014-03-16
Posts: 323

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...

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

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#430 2019-09-14 18:47:02

individ
Member
Registered: 2014-03-16
Posts: 323

Re: Formulas for the solution of Diophantine equations.

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

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

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#431 2019-12-03 20:03:19

individ
Member
Registered: 2014-03-16
Posts: 323

Re: Formulas for the solution of Diophantine equations.

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