Rational Number as Power of Number with Itself
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This theorem requires a proof..
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Theorem
Every rational number in the interval $\left({\left({\dfrac 1 e}\right)^{\frac 1 e} \,.\,.\, +\infty}\right)$ can be written either as:
- $a^a$ for some irrational number $a$
or as:
- $n^n$ for some natural number $n$.
Proof
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Sources
- March 2012: J. Marshall Ash and Yiren Tan: A rational number of the form $a^a$ with $a$ irrational (The Mathematical Gazette Vol. 96: 106 – 109)
