Can we prove that every entire one-to-one function is linear?
Entire one-to-one functions are linear
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complex-analysis
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1http://en.wikipedia.org/wiki/Picard_theorem (which is overkill if this is homework or something) – 2011-03-29
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2Maybe you can use the [Weierstrass Factorization Theorem](http://en.wikipedia.org/wiki/Weierstrass_factorization_theorem#The_Weierstrass_factorization_theorem)? – 2011-03-29
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4By 1-1, do you mean injective or bijective? – 2011-03-29
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0By the way... you should edit the question title, Petey, to remove the ugly typo! – 2011-03-29
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1@Arturo: you should let OPs do *some* of the fixing! It is a very instructive activity :) – 2011-03-29
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1@Mariano: But it *bugs* me so... – 2011-03-29
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0I know :) ${}{}$ – 2011-03-29
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1See also http://math.stackexchange.com/q/168629 – 2012-07-09