Question 28
Let $n$ be a fixed positive integer. Show that for only nonnegative integers $k$, the diophantine equation
$$
x_{1}^{3} + x_{2}^{3} + \cdots + x_{n}^{3} = y^{3k+2}
$$
has infinitely many solutions in positive integers $x_{i}$ and $y$.
$$
x_{1}^{3} + x_{2}^{3} + \cdots + x_{n}^{3} = y^{3k+2}
$$
has infinitely many solutions in positive integers $x_{i}$ and $y$.