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Empty
 one year ago
Solve:
f(x,y)*f(y,x)=f(x,y)+f(y,x)
Empty
 one year ago
Solve: f(x,y)*f(y,x)=f(x,y)+f(y,x)

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Empty
 one year ago
Best ResponseYou've already chosen the best response.2I promise to share the solutions I've found if you try. And my answers aren't trivial, they're dependent on x and y.

Empty
 one year ago
Best ResponseYou've already chosen the best response.2So here's the answer I found: \[f(x,y)=1+\log_xy\] I honestly have no clue how I would find this sort of thing naturally, it came up when I was considering some interesting properties of logarithms, such as: \[\log_a b \log_b a = 1\] \[\log_a b \log_b c \log_ca= 1\] Specifically I've just been looking for something so that \[f(a,b) * \log_a b = \delta_{ab}\] since this could be used to factor any number possibly easily with linear algebra.
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