# Many numbers with pairwise differences squares

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.

• Just one unless you consider only the positive differences. – W-t-P Oct 19 at 20:23

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.