# Tagged Questions

Questions on the number-theoretic functionality of Mathematica.

69 views

### Numerical testing of Hardy's inequality

I want to check the following, Hardy's most fundamental inequality, by using Mathematica: $$\sum_{n=1}^\infty \left(\frac{A_n}{n}\right)^p<\left(\frac{p}{p-1}\right)^p\sum_{n=1}^\infty a_n^p$$ ...
150 views

### Miller-Rabin algorithm [closed]

I want to implement the Miller-Rabin algorithm in Mathematica to check if a number is prime with at least 99.99% probability. I used this: ...
316 views

### Finite Field matrix rank calculation

How does one define a matrix over $\mathrm{GF}(p^r)$ in Mathematica in order to compute rank? I am working with $\mathrm{GF}(2)$?
5 views

### A question about the existence of [migrated]

Maybe a stupid question: I wonder if there exists such a k satisfying the following equation: Let $p_1,p_2,p_3$ be prime numbers and $0\leq x_1<p_2$, $0\leq x_2<p_1$,$0\leq x_3<p_3$. If $x_1$...
348 views

### Why is Mathematica getting this modular root wrong?

First, note that $4^{96}\equiv 96 \pmod {100}$. Mathematica claims that PowerMod[96, 1/96, 100] has no integer solutions. Even more obviously wrong, I get ...
57 views

### Get Mathematica to solve Modular Arithmetic problem [closed]

How would I get Mathematica to solve something like this for $x$? $4x \equiv 1 \pmod 5$
82 views

### Factor a polynomial Root into Roots of smallest possible degree

Suppose I have a polynomial Root representing an algebraic number. I want to represent it (if possible) as a product of several polynomial ...
94 views

### Check Zagier theorem about Mahler's measure

I want to check the following theorem by using Mathematica: (from Heights of Polynomials and Entropy in Algebraic Dynamics, page 22) $\textbf{Theorem}.$ Let $\omega$ denote a primitive $6th$ ...
61 views

### How can I implement Jordan's totient function?

How can I implement Jordan's totient function? It is a generalization of Euler's Phi function.
175 views

### Visualisation of the field of algebraic numbers in the complex plane

Hot to plot the field of algebraic numbers in the complex plane? In this picture, the color of a point indicates the degree of the polynomial of which it’s a root: red = rational numbers ...
45 views

### Efficiently create a list of factors of consecutive integers

I'm interested in a scalable (read: sublinear) algorithm for producing the list of integer factors of each integer from 1 to n. ...
61 views

### Are there any Mathematica programs on or about the LMFDB Archive?

I would like to explore the LMFDB Archive with L-functions using Mathematica. Is there any Mathematica sample code available to get me started?
135 views

### Is it better to completely forget about the existence of PowersRepresentations?

I noticed that in several cases the performance of PowersRepresentations is hugely worse than that of IntegerPartitions. (Mma 10....
90 views

### FrobeniusSolve: how does it work?

Can someone suggest any reference to read? I would like to understand how the algorithm works.
211 views