Fall 2018, problem 73
For all positive integers $n$ and $k$, define $F(n,k)=\sum_{r=1}^n{r^{2k-1}}$. Prove that $F(n,1)$ divides $F(n,k)$.
For all positive integers $n$ and $k$, define $F(n,k)=\sum_{r=1}^n{r^{2k-1}}$. Prove that $F(n,1)$ divides $F(n,k)$.