Problem 773

Erdős Problem #773: declared status 'open'. Formalized: no. What is the size of the largest Sidon subset $A\subseteq\{1,2^2,\ldots,N^2\}$? Is it $N^{1-o(1)}$? Current best: The lower bound was improved to$$\lvert A\rvert \gg N^{2/3}$$by Lefmann and Thiele [LeTh95]. Prize: no. OEIS: A390813. Tags: number theory, sidon sets, squares.