Popular differences for right isosceles triangles

Vjekoslav Kovač

For a subset $A$ of $\{1,2,\dots ,N{\}}^2$ of size $\alpha N^2$ we show existence of $(m,n)\ne (0,0)$ such that the set $A$ contains at least $({\alpha }^3-o(1))N^2$ triples of points of the for…