Discussion of TPID 6

[nuninho1980]

I think that the conjecture is false.
First, the numerical computation have to be carried out with much more precision.
The solution for x in \( {}^{1000}x = 1000 \) is approximately 1.44467831224667 which is higher than e^(1/e)
The solution for x in \( {}^{10000}x = 10000 \) is approximately 1.4446796588047 which is higher than e^(1/e)
As n increases, x increasses very slowly.
But, in any case, x is higher than e^(1/e) = 1.44466786100977

Second, on a more theoretical viewpoint, if x=e^(1/e), the limit of \( {}^{n}x \) is e , for n tending to infinity. So, the limit isn't = n , as expected.

The solution for x in \( {}^{1000}x = 1000 \) is approximately 1.44467831224667 -> is not correct! but yes - \( {}^{1000}x = 1000 \Rightarrow \) x=1.44467829141456

The solution for x in \( {}^{10000}x = 10000 \) is approximately 1.4446796588047 -> is not correct but yes - \( {}^{10,000}x = 10,000 \Rightarrow \) x=1.4446679658595034

you mistake!?!! eheheh! lool

\( {}^{100,000}x = 100,000 \Rightarrow \)x=1.444667862058778534938

therefore, the conjecture is NOT false!

I calculated the numbers corrects by program "pari/gp".