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Another nice reference (with a short proof) isin

G. Greiter, A simple proof for a theorem of Kronecker, Amer. Math. Monthly 85 (1978), no. 9, 756–757.

The proof in this paper is related to the proofs given above by Kevin and David, but is a bit more elementary.

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Another nice reference (with a short proof) is in

G. Greiter, A simple proof for a theorem of Kronecker, Amer. Math. Monthly 85 (1978), no. 9, 756–757.