The Fibonacci numbers are not a Heilbronn set

Daniel Shiu

For a real number $\hat{I}¸$, let $\Vert \hat{I}¸\Vert$ denote the distance from $\hat{I}¸$ to the nearest integer. A set of positive integers $\mathcal{H}$ is a Heilbronn set if for every $α\in \mat…