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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

3 votes
1 answer
933 views

Can $(\log\log m)/(\log\log n)$ be rational?

If $m, n$ are two different positive integers, is it true that the ratio $\displaystyle \frac{\log\log m}{\log\log n}$ is necessarily irrational? By $\log$ I mean the logarithm in base $e$ (not base …
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