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.
integer solutions of an equations
2
$\begingroup$
number-theory
elementary-number-theory
diophantine-equations
-
0either two are odd and one is even, or all three are even – 2012-11-03
-
0Why 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 editing – 2012-11-03
-
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
-
0A 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