In the paper, motivated by the generating function of the Catalan numbers in combinatorial number theory and with the aid of Cauchy’s integral formula in complex analysis, the authors generalize the ...

A nonzero rational number is called a cube sum if it is of the form a³ + b³ with a, a,bϵℚx. In this paper, we prove that for any odd integer k ≥ 1, there exist infinitely many cube-free odd integers n ...