# divisible by 5050

For how many integers k in the set $${1,3,5,7...,97,99}$$ Is $$\sum_{n=1}^{100} (n^{k})$$ divisible by $$5050$$? you can think in this direction : find out the remainder when $$x^{odd}+y^{odd}$$ is divided by $$x+y$$.

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