On simple additive configurations in random sets

On simple additive configurations in random sets

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Hoi H. Nguyen, Rutgers University
Fine Hall 224

We show that with high probability a random subset of $[n]$ of size $\theta(n^{1-1/k})$ contains two elements $a$ and $a+d^k$, where $d$ is a positive integer. As a consequence, we prove an analogue of the Sarkozy-Furstenberg theorem for a random subset of $[n]$.