Irrationality of powers of $\pi$

Everyone recognizes that $\pi$ is an illogical number, and also one can describe this page for the evidence that $\pi^{2}$ is additionally illogical.

What concerning the highers powers of $\pi$, definition is $\pi^{n}$ illogical for all $n \in \mathbb{N}$ or does there exists a $m \in \mathbb{N}$ when $\pi^{m}$ is sensible.

2019-05-09 11:30:50
Source Share
Answers: 1

What Robin meant :

If $\pi^{n}$ was sensible, after that $\pi$ would certainly not be transcendental, as though the origin of $ax^{n}-b = 0$ for some integers $a,b$.

2019-05-10 07:33:00