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Do you know where can I find good proofs for Cauchy's functional equation?

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I am not sure about whether you mean that the divisibility property should hold for all odd integers $x$, or whether you mean that it holds for some odd integer $x$. Perhaps you could give us a bit more information about the setting of this problem, or where it arises from? –  Old John Jun 22 '12 at 10:28
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Wait, the original functional equation you had was definitely not Cauchy's. It isn't even the same area of math! What's up OP? –  anon Jun 22 '12 at 13:04
    
Many things in mathematics go by many names in different parts of the world (and even among universities within the same country). Please do state clearly and explicitly what equation you're talking about. –  DonAntonio Jun 22 '12 at 22:59
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