Problem 1103

Erdős Problem #1103: declared status 'open'. Formalized: no. Let $A$ be an infinite sequence of integers such that every $n\in A+A$ is squarefree. How fast must $A$ grow? Current best: In [Er81h] he asked whether there is an infinite sequence of integers $A$ such that, for every $a\in A$ and prime $p$, if$$a\equiv t\pmod{p^2}$$then $1\leq t<p^2/2$. A superior lower bound of $a_j \gg j^{15/11-o(1)}$ had earlier been found by Konyagin [Ko04] when considering the finite case [1109]. Prize: no. OEIS: A392164. Tags: number theory.