TITLE: Many numbers with pairwise differences squares
QUESTION [9 upvotes]: 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.

REPLY [8 votes]: 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.