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If f is analytic in $|z| \leq1 $ and satisfies $ |f(z)| = 1$ on $|z| = 1$ prove that f is a rational function. I need a clue how to think about this? should i use the fact that f can be written as a power series?

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marked as duplicate by choco_addicted, user296602, Claude Leibovici, colormegone, Watson Apr 24 '16 at 8:56

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