Infinite exponents of x x .

Number Theory Level 2

How many values of x x satisfy the equation x x x ⋅ ⋅ ⋅ = x x^{x^{x^{\cdot^{\cdot^{\cdot}}}}} = x ?

x x must be a positive integer.


The answer is 1.

. . by . . , 14, South Korea

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1 solution

. .
Feb 27, 2021

Only 1 1 satisfies the equation.

0 0 0 ⋯ is undefined. { { 0 ^ { 0 } } ^ { 0 } } ^ { \cdots } \text { is undefined. }

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Also 1 and their squares and another is sqrt(2)

Elijah Frank - 3 months, 2 weeks ago

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Well, the question says that x x must be a positive integer.

Elijah L - 3 months, 1 week ago

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