2
$\begingroup$

Now I came with an equation to find the solutions in integers. Not aonly that, I would like to know other types of solutions (if exists). Find the solutions and method of solving the equation $p^3 - 2pqr = q^3 + r^3$. Where the $p, q, r$ may be integers.

  • 0
    either two are odd and one is even, or all three are even2012-11-03
  • 0
    Why do you want to solve this Diophantine equation?2012-11-03
  • 0
    @F'OlaYinka! there is no restriction on even and odd. I am looking integral solutions and the method of solving such equations. Kindly help me in this regard.2012-11-03
  • 0
    @vmr, F'Ola is saying every solution satisfies those restrictions. Can't you see why there can't possibly be a solution with all three odd?2012-11-03
  • 0
    @GerryMyerson!I know it. I said, how you can determine those solutions in numerical. The solutions may be odd, does not matter. How to solve such equation to list all the solutions (may be odd).2012-11-03
  • 0
    @JonahSinick! This only my out most interest. nothing else.2012-11-03
  • 0
    @vmr I have corrected the LaTeX in your question. You need to put the dollar sounds around complete formulae, rather than individual parts of formulae.2012-11-03
  • 0
    @OldJohn! Thank you for editing2012-11-03
  • 0
    @vmrfdu123456 , you seem to be missing big time what both F'Ola and Gerry told you: as a first, rather important, step to solve your equation, you have to realize that it **must** be that either two of the numbers in an eventual solutions **must** be odd and one even, or else all three **must** be even. If you don't understand this then you'll hardly understand an eventual solution to your problem.2012-11-03
  • 0
    @ vmrfdu123456, Why this particular Diophantine equation rather than another?2012-11-03
  • 0
    @DonAntonio! I understand that, please explain the method to get such solutions, when two of them are odd.2012-11-05
  • 0
    A maple search didn't find any solutions where $p,q,r$ are between $-100$ and $100$ (except for the trivial solutions where $pqr=0$ and the nonzero have same magnitude).2013-01-23

1 Answers 1