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So if you have a field Div F = 0, then F = Curl A. That's easy.

Here is the confusing part: Then he says integral over the surface of F.da is independent of surface and integral over the surface of F.da =0 for a closed surface.

I am not sure how to prove these things. I get 0 as a result no matter what because of the levi-cevita symmetry. Please could somebody let me know what I am doing wrong.

Thank you so much.

-DA