This post is a sincere request for help. I assume that the following problem can be represented by a differential equation and that only a mathematician can solve it.(adsbygoogle = window.adsbygoogle || []).push({});

Let A={real numbers x such that |x|<1}

Let S={real numbers Z such that 1 < Z < infinity}

Define ^ on A by the rule x^y = (x+y)/(1+xy).

It follows that (A, ^) is an Abelian group:

x^y=y^x

x^0=x

x^(-x)=0

x^(y^z)=(x^y)^z

I'm looking for a function from AxS->S (also written ^) such that, for any x, y, in A and any Z in S:

x^(y^Z) = (x^y)^Z

0^Z=Z

x^Z > Z if x>0

x^Z < Z if x<0

Thanks

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# Only a Mathematician Can Solve This Equation

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