A square-difference-free set is a set of integers in which the absolute difference between any two distinct members is not a positive
square number. For example, 
is square-difference-free, whereas 
is not.
The Furstenberg-Sárközy theorem implies that the maximum size 
of a square-difference-free subset
of 
satisfies 
.
-Intersective Polynomials." Acta Arith. 157,
69-89, 2013.