Binary Quadratic Forms in Difference Sets

Alex Rice

We show that if $h(x,y)=a{x}^2+bxy+c{y}^2\in \mathbb{Z}[x,y]$ satisfies $\Delta (h)=b^2-4ac\ne 0$, then any subset of $\{1,2,\dots ,N\}$ lacking nonzero differences in the image of $h$ has s…