6
$\begingroup$

How many different natural numbers are there such that the difference of any two is a perfect square?

I could find that with 'sums' instead of 'differences' this has been asked by Erdos and L. Moser (see Guy: Unsolved Problems in Number Theory, 3rd ed., p. 268), and that is open, with six being the current record.

$\endgroup$
  • 1
    $\begingroup$ Just one unless you consider only the positive differences. $\endgroup$ – W-t-P Oct 19 at 20:23
8
$\begingroup$

Four is possible, an example is $0,451584,462400,485809$. This solution comes from the example of a cuboid with integer sides, space diagonal and two out of three face diagonals given here. I don't know for $5$ or more but it is probably a very hard question.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.