# Tagged Questions

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### Number of generators of ideal if quotient field has certain transcendence degree

I am trying to prove a result which is used in A. Macintyre and A. J. Wilkie (1995), 'On the decidability of the real exponential field', in Odifreddi, P.G., Kreisel 70th Birthday Volume, CLSI, p. ...
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### Transcendence of solutions of $\sum_{i=1}^n a_i b_i^x = 1$

I am currently doing things related to the Akra–Bazzi theorem. One element in that theorem is the following: For $n>0$ and sequences of real numbers $a_i, b_i$ of length $n$, where all $a_i>0$ ...
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### Random Sequence : Definition of [closed]

"A sequence of bits is random if there exists no Program shorter than it which can produce the same sequence." ~ Kolmogorov Q: How do the digits of Pi fall as a random sequence based on the above ...
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### Why is it hard to prove that the Euler Mascheroni constant is irrational?

Philosophically why should proving that $\gamma$ is irrational (let alone transcendental) be so much harder than proving $\pi$ or $e$ are irrational?
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### What was Lambert's solution to $x^m+x=q$?

I've been thinking about Lambert's Trinomial Equation quite a bit, and I want to see his solution. The only solution I could find was in Euler's form, and I still don't quite understand how he got ...
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### quasi periodic continued fractions and powers of e, tanh, tan

It is well known that some transcendental numbers like e.g. rational multiples of $e^{2/n}$ with $n\in\mathbb N$, when written as regular continued fractions (R.C.F.), yield what can be called a ...
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### Transcendental numbers that are “suspected” to be algebraically dependent without conjectured relation?

I am experimenting with a solver for finding algebraic dependencies and would like to test it on more data sets. Are there transcendental numbers that are "suspected" to be algebraically dependent ...
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### Is this seemingly novel irrational constant also transcendental?

I recently discovered a constant that is constructed as follows: $\chi=\sum_{n=1}^\infty (\frac{\cos{n}}{2|\cos{n}|}+\frac{1}{2}) 2^{-n}$ Furthermore I can prove that it is an irrational number ...