If there are so many of these equations out there with solutions why not provide one, using some small numbers. I suggested sqrt(2) = x, and pi = 7. then, if you find a value for z with n > 2,matt grime said:But there are infinitely (uncountably) many positive real solutions to the equation
for all n in N.
So your proof which allegedly shows these don't exist, is wrong. That is the reason why no one appears to be taking it seriously your proof can be used to show that something is false when it is actually true.
I don't understand what on earth your getting at with claiming a counter example with x=1 is trivial, and therefore not something to be considered. It is a counter example to a claim you made. It is *trivial* in the sense that it easy to show, however x=1 was not picked for any special reason other than it was a simple small example. (n=1 is trivial in the sense of FLT.)
z = [sqrt(2)^n + pi^n]^(1/n)
For a simple solution we can find this value with n = 7:
z = (11.3137085 + 3020.293228)^(1/7)
z = 3.143271116
this is a little bit more than the original constant value of y = pi