Sárközy's Theorem for Fractional Monomials

Maximilian O'Keeffe

Suppose $A$ is a subset of $\{1,\dots ,N\}$ which does not contain any configurations of the form $x,x+\lfloor n^c\rfloor$ where $n\ne 0$ and $1<c<\frac{6}{5}$. We show that t…