I am trying to prove that $$\frac{\sum_{n=1}^{t} n^{2r+1}}{\sum_{n=1}^{t} n}$$ is an integer for $r,t\geq 1$.
I have managed to show this for $r=1$ and $r=2$ but I don't know where to go from here. How do I prove this for all $t$ and $r$?
Thank you!
2026-03-27 13:25:49.1774617949
Proving that $\frac{\sum_{n=1}^{t} n^{2r+1}}{\sum_{n=1}^{t} n}$ is an integer
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