Let $f$ and $g$ be entire functions such that $e^f + e^ g=1$ then how to show $f$ and $g$ are constant. I am having trouble in proving these. any help would be appreciated. Thanks in advance.
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1$e^f\ne 0$ and hence $e^g\ne 0$ and $1$ - Contradicts Picard's Little Theorem. â Yiorgos S. Smyrlis Jun 19 '17 at 19:59
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1Thanks I got it. I have another question.I think it ia true.Is it? â math is fun Jun 19 '17 at 20:13
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1Let f and g be entire functiona such that (fâ˘g)(z) is a polynomial .I think both f and g are polynomials . â math is fun Jun 19 '17 at 20:14