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Diophantine Linear Equation ?

lvl107
20-Turquoise

Diophantine Linear Equation ?

Hello Everyone.

1.PNG2.PNG

                                                             --//--

3.png

                                                                        --//--    

4.png

                                                                                  --//--

5.png

Thanks in advance for your time and help.

Regards.

4 REPLIES 4
-MFra-
21-Topaz II
(To:lvl107)

The determinant gives an equation with two unknowns. However, if I add another one relating to the next ratio, I obtain a non-homogeneous linear system of equations in the unknowns X and Y, of which there is a solution. What do you think?

lvl107 answer.jpg

lvl107
20-Turquoise
(To:-MFra-)

Thanks for your time, MFra. I guess we should consider something about: 1.png . Copy and paste your screenshot, it seems look like the following:

2.PNG3.PNG4.png

Thanks your time again.

Best Regards.

Loi.

-MFra-
21-Topaz II
(To:lvl107)

I know it's not the answer you are looking for, furthermore, some are negative and aren't diophantine solutions, but it's already something ....

lvl107 answer 1.jpg

Instead of defining a linear non-homogeneous system of equations with constant coefficients in two variables, in the same way, one should define such a system in N equations in N diophantine unknowns. I don't know if that's possible. 

In the group "Gruppo di Matematica" of FB, there is a professor (Domenico Annunziata) who has written a book dedicated to Diophantine equations, you could turn to him for clarification.

LucMeekes
23-Emerald III
(To:lvl107)

I think this shows that Maple will happily solve your equations:

LucMeekes_0-1618259088745.png

Success!
Luc

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