Ruzsa's sumset conjecture for finite sets of squares
For a finite set of squares, write . Ruzsa's conjecture. For every ,
The source states that Chang's conjecture implies this one, while the Bombieri--Lang conjecture yields only weaker bounds; its general validity remains open.
References
Primary source
Javier Cilleruelo and Andrew Granville, “Lattice points on circles, squares in arithmetic progressions and sumsets of squares”, arXiv:math/0608109 (2006).
Progress summary
Never refreshed
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
No solutions have been posted yet.