(In reply to
re(7): Solution? by Richard)
I don't like the x=4 solution either, I only mentioned it because you were looking for other x values that would satisfy the equation for some fixed n. But I think it is perfectly reasonable to say sqrt(64) is 8. In other words, would you say x=4 is one of the roots of:
f_2: x^4  4x^2  192 = 0
f_3: x^8  8x^6 + 16x^4  576x^2  27648 = 0
..,? If you consider these nonrecursive cases of the problem then x=4 is certainly a solution.
I don't like x=4 as a solution because:
a) it doesn't hold for f_0(x), and
b) if you assume f_n(x) = 8, then f_n+1(x) is unsolvable.

Posted by tomarken
on 20061120 01:26:34 