# Questions tagged [nt.number-theory]

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

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### Tannakian fundamental group of automorphic representations

Let $\mathcal{C}_{\mathrm{aut}}(G, F)$ be the category of automorphic representations of a connected reductive group $G$ over a number field $F$. If this is a Tannakian category, it has an associated ...
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### Finding elements in a real extension of $\mathbb{Q}$ that are close to some number in $\mathbb{R}$

Let's consider a set of numbers that one knows to high precision, and one knows or has a strong suspicion that `exact versions of these numbers' (see below) belong to a real extension of $\mathbb{Q}$. ...
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### Magic hourglass of squares hyperelliptic equation

I have been looking into the problem of the magic square of squares, or more specifically, the magic hourglass of squares, like so: $a^2$ $b^2$ $c^2$      $d^2$ $e^2$ $f^2$ $g^2$ ...
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### Modulo $2$ binomial transform of A243499 applied $k$ times

Let $m \geqslant 1$ be a fixed integer. Let $f(n)$ be A007814, exponent of highest power of $2$ dividing $n$, a.k.a. the binary carry sequence, the ruler sequence, or the $2$-adic valuation of $n$. ...
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### Modulo $2$ binomial transform of A124758

Let $f(n)$ be A153733, remove all trailing ones in binary representation of $n$. Here \begin{align} f(2n)& = 2n\\ f(2n+1)& = f(n)\\ \end{align} Then we have an integer sequence given by \begin{...