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if $e$ and $π$ are irrational numbers, is $\frac{e}{\pi}$ irrational too?

How to prove it?

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    I think this is an open question (nobody knows). also, note that in general the quotient of two irrational numbers may or may not be irrational – Albert Dec 18 '19 at 08:15
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    Welcome to MSE. On a related note, you may find MathOverflow's [Irrationality of $ \pi e, \pi^{\pi}$ and $e^{\pi^2}$](https://mathoverflow.net/questions/40145/irrationality-of-pi-e-pi-pi-and-e-pi2) interesting. – John Omielan Dec 18 '19 at 08:15
  • https://math.stackexchange.com/questions/159350/why-is-it-hard-to-prove-whether-pie-is-an-irrational-number – 49-49 Dec 18 '19 at 08:25

1 Answers1

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It is currently unknown whether $\frac{e}{\pi}$ is irrational. See https://en.wikipedia.org/wiki/Irrational_number#Open_questions

lisyarus
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