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Can anyone help me with the following question? Let $X$ be a smooth, projective algebraic variety. Let $D$ be an effective divisor on $X$ and $m$ an integer.

Under which conditions there exists a line bundle $L$ such that $\mathcal{O}_X(D)=L^m$?

There is of course the obvious one: $m$ should divide de degree of $D$. Is that sufficient?

You can assume that $D$ has normal crossings but I don't think that matters for this particular question.

Thanks! (and Merry Christmas)

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