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15
142
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How to solve $x^{x^{x^{x^{2010}}}} = 2010$

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#exponentiation #power-towers
257
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How to compute $\,3^{3^{3^{\:\!\phantom{}^{.^{.^.}}}}}\!\!\!\!\bmod 46,$ for power tower height $2020$?

Published on
#elementary-number-theory #modular-arithmetic #tetration #power-towers
272
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Complexity of repeatedly applying Euler's totient

Published on
#modular-arithmetic #asymptotics #computational-complexity #totient-function #power-towers
193
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Alternating power sequence

Published on
#sequences-and-series #power-towers
82
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Find the last digits of $a_{2009}$, and of $b_{2009}$.

Published on
#sequences-and-series #modular-arithmetic #decimal-expansion #tetration #power-towers
39
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Comparison of power towers with different bases

Published on
#power-towers
41
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Almost integer with nested radicals and power tower .

Published on
#power-series #nested-radicals #constants #power-towers
468
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Convergence of probabilistic power tower $e^{\pm e^{\pm e^{...}}}$

Published on
#probability #convergence-divergence #power-towers
98
Views

Why it were conjectured that $e^{e^{^e{^{79}}}}$ is not an integer only for $n=79$ ? any non trivial characterization?

Published on
#prime-numbers #exponentiation #power-towers
64
Views

$i^i\in\mathbb R$

Published on
#complex-numbers #power-towers
374
Views

Does the infinite power tower $x^{x^{x^{x^{x^{x^{x^{.{^{.^{.}}}}}}}}}}$ converge for $x < e^{-e}$?

Published on
#convergence-divergence #power-towers
118
Views

"Shooting Room" ratio when selection sizes grow tetrationally

Published on
#sequences-and-series #tetration #power-towers #hyperoperation
203
Views

Is it possible to express $\int_{0}^{1-\epsilon}\left(\sqrt{1-x^2}^{\sqrt{1-x^2}^{\cdots}}\right) dx$ in elementary functions?

Published on
#real-analysis #integration #power-towers
103
Views

how many $\sqrt{2}^{\sqrt{2}^{\sqrt{2}\ldots }}$

Published on
#roots #graphing-functions #tetration #power-towers
751
Views

Why do $x^{x^{x^{\dots}}}=2$ and $x^{x^{x^{\dots}}}=4$ have the same positive root $\sqrt 2$?

Published on
#sequences-and-series #analysis #power-towers

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