# Tagged Questions

Questions on basic arithmetic involving numerical quantities only. Questions involving variable values (other than the result of the operation) should be placed under the (algebra-precalculus) tag.

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### Infinite sum involving $q$-adic representations of whole numbers and $q$-factorial numbers

Let $q \in \mathbb{N}_{\geq 2}$. For $n \in \mathbb{N}_0$, let $$\mathrm{fac}_q(n) := \prod_{i=1}^n (1+q+\dots+q^{i-1}) = \prod_{i=1}^n \frac{q^i-1}{q-1}$$ be the $q$-factorial of $n$. In particular, ...
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### Does this operation have a name?

For a field $F$, define the binary operation $\parallel :(F\mathbb{P}^1 \times F\mathbb{P}^1 \setminus\{(0,0)\}) \to F\mathbb{P}^1$ by $$a \parallel b = \frac{1}{\frac{1}{a} + \frac{1}{b}}.$$ This ...
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### Is there a numeral system that makes both addition and multiplication easy?

Decimal positional notation, the system for writing numbers we all use every single day, makes addition very easy by transforming it from a computation to a repeated operation on individual digits (...
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### Quotition versus partition

This new Wikipedia article may look different by the time the reader of this question sees it. For now, it says $6\div 2$ can be construed in either of two ways: "How many parts of size $2$ must be ...
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### Extention of Euclid's GCD Algorithm. (The Art of Computer Programming, Volume 1, Edition 3, Section 1.2.1, Exercise 12)

Euclid's GCD algorithm which is used to find GCD of two input numbers, say, $c$ and $d$, needs the inputs to be positive integers. Exercise 12 provides an extension to this algorithm and allows $c$ &...
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### Does anyone know of a Mental Math Game for blind students?

I'm looking for any computer game made for blind students where the math exercises are asked through a computer's speaker and answered through a microphone by the student. Unlike normal math games, ...
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### Application of GRR in number theory

In Neukirch Book Algebraic Number Theory page 254, states the Grothendieck-Riemann Roch-Theorem, but missing of applications. Do you know references for applications for this theorem, or may be ...
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### Shepherdson's model for Open Induction

In the paper "A Non-Standard Model for a Free Variable Fragment of Number Theory", Shepherdson constructs a recursive model for a fragment of arithmetic known as "Open Induction". I would like to ...
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### Is there a name for this property of multiplication (and other functions)?

Suppose $x,y \in \mathbb{R_+}, x<y$, and $0 < \varepsilon \leq (y-x)/2$. It seems to me that $xy < (x+\varepsilon)(y-\varepsilon)$ and equivalently that $(x+\varepsilon)(y-\varepsilon)$ is ...
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