# Tagged Questions

Questions about numbers expressible as the quotient of two integers. For questions on determining whether a number is rational, use the (rationality-testing) tag instead.

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### Is the value of $\log_27$ a rational number?

Is $\log_27$ a rational number?
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### Minimizing rational solutions of $x^3+y^3=9$

I´m trying to solve this problem: An old alchemist had two sphercial flasks, one with a circunference of 12 inches and the other with a circunference of 24 inches. He desired to transfer their ...
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### If $\cos\pi\theta$ is algebraic and $\theta$ is irrational, what is the set of possible $\theta$?

I know that $a= \cos \pi \theta$ is an algebraic number ($\theta$ is rational). I want to prove that if $\cos\pi\theta$ is rational, then the possible only possible values of $\theta$ are $0,±1/2,±1$ ...
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### Let $H = \{2^m : m \in \mathbb{Z}\}$ & define a relation $R$ on the set $\mathbb{Q^{+}}$ of positive rationals by $a\mathbin{R}b$ iff $a/b \in H$.

Let $H = \{2^m : m \in \mathbb{Z}\}$ and define a relation $R$ on the set $\mathbb{Q^{+}}$ of positive rational numbers by $a\mathbin{R}b$ if and only if $a/b \in H$. Prove that $R$ is an equivalence ...