I tried for a few hours to come with a proof that $π^e$ is irrational. I mainly tried with the method "proof by contradiction" and didn't use calculus at all, but couldn't come up with a proof.
Can anyone give a proof that $π^e$ is irrational? I would appreaciate if it was without using calculus. because that's more fun, but it's completly fine using calculus too :) Just want to see a proof.
Thanks in advance!