Would it be possible to prove that there is an equation that includes a number N of unknown numbers that are all equal, between 0 and 1 and whose sum is equal to 1 ? And to find this equation ?
I don't know if the problem is well defined and if it's possible. It works with A - B = 0 with A = B = 0.5 but I'm struggling to prove and extend it. I'm not sure that it would be "legal" to do any multiplication or division.
Regards
You can certainly do $$\left(a-\frac 13\right)^2+\left(b-\frac 13\right)^2+\left(c-\frac 13\right)^2=0$$ with the obvious generalization to $n$ variables.