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Helmhotz's Theorem states that any vector field whose divergence and curl vanish at infinity can be written as the sum of may be written as the sum of an irrotational part and a solenoidal part - I.e. as the sum of the curl of a vector field and the grad of a scalar field.

Not exactly the same but kind of close

What is that theorem? Does anyone know this? Is it true that if I define the divergence and the curl that the vector fields are unique to an additive constant? If so then I would like to see a proof.

Thanks

Pete