TITLE: English reference for a result of Kronecker?
QUESTION [26 upvotes]: Kronecker's paper Zwei Sätze über Gleichungen mit ganzzahligen Coefficienten apparently proves the following result that I'd like to reference:

Let $f$ be a monic polynomial with integer coefficients in $x$. If all roots of $f$ have absolute value at most 1, then $f$ is a product of cyclotomic polynomials and/or a power of $x$ (that is, all nonzero roots are roots of unity).

However, I don't have access to this article, and even if I did my 19th century German skills are lacking; does anyone know a reference in English I could check for details of the proof?

REPLY [7 votes]: In case anyone is interested, here's a run-down of the history of this result and a comparison of available proofs, as far as I could uncover in a rainy evening.

To be clear, Kronecker's original article, cited in P.A. Damianou's article, actually proves the following: given a monic polynomial with integer coefficients all of whose roots have norm 1, the roots are all roots of unity.
Kronecker's argument (in German) is almost identical to David Speyer's above. Both are almost identical to P.A. Damianou's---Damianou seems to have largely translated Kronecker, I think.
G. Gretier's Monthly article (cited by Damianou), J. Spencer's Fibonacci Quarterly article (cited by Greiter), and Kevin Buzzard's argument in brackets all prove this statement in related but different ways. Greiter uses companion matrices and diagonalization. Spencer's argument is the longest and builds a Fibonacci-type linear recurrence out of such a polynomial, using the corresponding Binet-type formula to show the recurrence must repeat.
Bombieri and Gluber's version is essentially a repackaging of Kronecker's argument in more number-theoretic language.
Polya and Szego's question 200 seems to be mostly just the theorem statement, though questions 198 and 199 are similar to the first part of Kevin Buzzard's argument.