# Tagged Questions

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### Conjecture on irrational algebraic numbers

Conjecture:
For every irrational algebraic number $q$ and natural number $b$, the representation of $q$ on base $b$ contains all the digits $[0,\dots,b-1]$.
Questions:
Has this conjecture been ...

**0**

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**0**answers

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### bounds of weighted sum of exponentials (related to Baker's theorem)

Given $n$ integers $a_1, \cdots, a_n$ and $n$ algebraic numbers $b_1, \cdots, b_n$, consider
$S=\sum_{i=0}^n a_i e^{b_i}$, the question is how to give a lower bound of $|S|$ assuming that $S\neq 0$, ...

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**1**answer

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### Rational points of non-rational curves

An algebraic curve (in this question) is the zero set $C = f^{-1}(X\ Y)$ of any polynomial $f\in\mathbb R[X\ Y]$; we say then that $f$ represents $C$. ...

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**1**answer

387 views

### How can we understand Baker's theorem about transcendence ?

We know that for algebraic $e^{it\pi}$, $t$ can not be algebraic irrational by
Baker's theorem, but his proof is analytic; is there some algebraic understanding for such fact? If $t$ is ...