Can Introductory Vector Calculus Prove C = Curl A?

[morangta]

Homework Statement

Given that the divergence of a vector C = 0, show that there exists a vector A such that C = curl A.

Homework Equations

See above.

The Attempt at a Solution

No clue. Can this be proved with introductory vector calculus? That's all I know, including many of the vector-calculus identities. I don't know anything about differential topology, Poincare's Lemma, etc.

I assume that somehow A has to be constructed, but that's as far as I get.

Thank you.

 

[physiks]

Homework Statement

Given that the divergence of a vector C = 0, show that there exists a vector A such that C = curl A.

Homework Equations

See above.

The Attempt at a Solution

No clue. Can this be proved with introductory vector calculus? That's all I know, including many of the vector-calculus identities. I don't know anything about differential topology, Poincare's Lemma, etc.

I assume that somehow A has to be constructed, but that's as far as I get.

Thank you.

What is ∇.(∇xA)?