Problem 170

Erdős Problem #170: declared status 'open'. Formalized: yes. Let $F(N)$ be the smallest possible size of $A\subset \{0,1,\ldots,N\}$ such that $\{0,1,\ldots,N\}\subset A-A$. Find the value of$$\lim_{N\to \infty}\frac{F(N)}{N^{1/2}}.$$ Current best: The lower bound is due to Leech [Le56], the upper bound is due to Wichmann [Wi63]. Computational evidence by Pegg [Pe20] suggests that the upper bound is the truth. Prize: no. OEIS: A046693. Tags: additive combinatorics.