Cube sum problem and an explicit Gross-Zagier formula
Cube sum problem and an explicit Gross-Zagier formula
A nonzero rational number is called a {\it cube sum} if it is of the form $a^3+b^3$ with $a,b\in{\Bbb Q}^\times$. In this paper, we prove that for any odd integer $k\geq 1$, there exist infinitely many cube-free odd integers $n$ with exactly $k$ distinct prime factors such that $2n$ is …