7
$\begingroup$

Equation

$$(2x^2+1)(2y^2+1)=4z^2+1$$

has no solutions in the positive integers. Its true?

Improve this question
$\endgroup$
3
  • 13
    $\begingroup$ There are no solutions according to Theorem 6 in Kashihara: Explicit complete solution in integers of a class of equations $(ax^2-b)(ay^2-b)=z^2-c$, Manuscripta Math. 80 (1993), 373-392. $\endgroup$
    – GH from MO
    Commented Jul 13, 2018 at 0:54
  • 3
    $\begingroup$ @GHfromMO Hey why didn't you type that as answer? My request would be to type your comment as an answer so that this question is removed from the unanswered list :) $\endgroup$
    – C.S.
    Commented Jul 13, 2018 at 14:22
  • $\begingroup$ I don't understand you $\endgroup$
    – witek
    Commented Jul 13, 2018 at 15:29

1 Answer 1

Reset to default
14
$\begingroup$

By popular demand, I turn my comment to an answer:

There are no solutions according to Theorem 6 in Kashihara: Explicit complete solution in integers of a class of equations $(ax^2−b)(ay^2−b)=z^2−c$, Manuscripta Math. 80 (1993), 373-392.

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .