is-there-a-general-solution-for-the-equation-x-x-x-x-n-times-x-m-with-x-gt-0-m-gt-0-

Question Number 77204 by mr W last updated on 04/Jan/20

i s t h e r e a g e n e r a l s o l u t i o n f o r

t h e e q u a t i o n

\underset{n t i m e s x}{x [x [x [x \dots]]]} = m

w i t h x > 0, m > 0 .

Commented by MJS last updated on 04/Jan/20

can we solve for all m, n ? I {don}^{'} t think so

you showed x [x [x [x]]] = 88 \Rightarrow x = 22 / 7

but x [x [x [x]]] = 87 seems to have no solution

it could be helpful to determine the set S_{n} \subset N

with y_{n} \in S_{n}, y_{n} = x {[x]}_{n times}

Commented by mr W last updated on 04/Jan/20

y o u a r e r i g h t s i r . f o r a g i v e n n t h e

e q u a t i o n {d o e s n}^{'} t h a v e s o l u t i o n f o r

e v e r y m . e . g . x [x] = 3 h a s n o s o l u t i o n .

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