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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