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Mick's rejected gem
On MSE my friend mick his equation has been closed.
He is angry about it.

I see the value of it.
And a potential link to tetration.

So for the sake of math, tetration , friendship and justice i post it here.


Find all the solutions $f(x)$ valid for $x>0$ and

$$exp(\int f(x) - f(x-1) dx) = f(x) -1$$

Thank you.

End quote

Here the integral starts at 0 and ends at x.

Just like integral f(x) dx means int_0^x f(T) d T .

You could argue about integration constant and abuse notation but its a very solid idea !!

Hopefully this has more succes here.

It reminds me of the Julia equation.



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