# Questions tagged [number-theory]

Questions on the number-theoretic functionality of Mathematica.

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### Extending the Definition of GCD [closed]

Suppose we have $q \in \sqrt[b]{a}$ for $a,b\in\mathbb{N}$ and $$q=\prod_{\underset{p \le q, \ i\le|p|, \ k\in \mathbb{N}}{p\in\text{prime},\ j_i,i\in\mathbb{N}}} {p}^{({j_i}/{k})}$$ $|p|$ is the ...
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### Prime factorization related functions: prime factor to its power and power of prime [duplicate]

FactorInteger can be used to perform prime factorization: FactorInteger[5^2 7^3 11^4] Results in: ...
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### Why does Solve lock up when trying to solve the quadratic equation with large integers?

Why does Solve lock up when trying to solve the equation ...
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### What is the best build-in function to pick or select given element in a huge list

im looking for a best and efficient function works like a search engine it takes for example m=5+6I ,then it goes searching in the list V={1,1+I,2+3I,...} until catch it . My Dr said to use "Select[]"...
314 views

### Efficient code for minimum integer with given number of factors

I'm seeking an efficient implementation of the number-theoretic function giving the smallest integer $n$ that has exactly $k$ factors (not necessarily prime): ...
149 views

### Finding $x$, the exponent of a $2^x$ when we need an specific output

Say we need a program Findx[n_Integer, m_Integer] where n is an integer from 1 to 9 and m is an integer from 1 to 1000. The output of the program is a number x, which is the exponent of 2 that ...
146 views

### Solving Diophantine equations 5 [closed]

Given a positive integers x,y,m would like to be able to find integer solutions z from Diophantine equation x^2-y^2 = m*z in Z. ---The proof,is divided in 4 sections---... x=2*k+1 ,y=2*h+1 with ...
61 views

### Problem in Counting the Number of Divisors with a Function [closed]

I want to create a function in mathematica which returns the number of divisors of a parameter x. So, I created the following function: d[x_] = Length[Divisors[x]]; And when I evaluate: d[1] d[2] ...
25 views

### Finding smallest domain within which variables can satisfy inequality

Given an arbitrary number of variables $\epsilon_i$ that can be picked from a domain $[0, W]$ and some inequality relation between all the variables $G(\epsilon_1, \epsilon_2, ...)$, is there some way ...
401 views

### Does Mathematica have a twin prime equivalent of PrimePi?

Well, it's all there in the title! I'd like to be able to plot the number of twin primes =<x. Is there an inbuilt function that can do this?
102 views

### How to find, load and use a legacy Mathematica package

Question: How to find, load and use a legacy Mathematica package from a previous Mathematica version? What is the preferred approach and process? Context: I am working through a set of examples in ...
40 views

### FunctionDomain in the Reals numbers [closed]

Why don't I obtain that $x$ belongs to the Reals? ...
87 views

### Simultaneous equation [closed]

How to solve Simultaneous equation in Mathematica: x^2 - (a^2 - 1)y^2 = 1 and y^2 - pz^2 = 1 where ...
88 views

### Number-theoretic function using Table

I'm trying to make a function to calculate the Log sum of primes over a limited range $1/2n$ to $n$ or Chebychev theta function over limited range $1/2n$ to $n$. This will be used only for even ...
312 views

### Find the order $m$ of a matrix ${\bf A}$ such that ${\bf A}^m= {\bf 1}$

I have a square matrix ${\bf A}$ defined over the field $\mathbb Z_2$ and I want to find its order such that ${\bf A}^m=1$. I tried using ...
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### How to define a function the Dirichlet L-function $L(s,\overline{\chi(5,2)})$ in Mathematica?

In Mathematica: The Dirichlet L-function with character $\chi(5,2)$, $L(s,\chi(5,2))$, is expressed as DirichletL[5,2,s] Let $\overline{\chi(5,2)}$ be the complex ...
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### François Viète's approximation to π

How do I program the approximation to π devised by François Viète, which is given by 2 * 2/Sqrt[2] * 2/Sqrt[2 + Sqrt[2]] * 2/Sqrt[2 + Sqrt[2 + Sqrt[2]]] * ... ...
42 views

### Question about using ParallelMap to speed up computations [duplicate]

First; I define two functions: ...
100 views

### Code for finding $a$ and $b$ such that $a b = 1 \mod 4$ [closed]

I need to find $a$ and $b$ such that $a b = 1 \mod 4$? I do not know how to write the code. Could someone help me?
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### Generating numbers palindromic in two number bases

The purpose of the code below is to generate numbers that are $2d+1$ digit palindromes in number base $b+1$, and are also palindromic in number base $b+3$, where: The ...
175 views

### Easy number theory problem

$p$ is an odd prime number，$S = \{x \mid 1 \leq x \leq 2p, x \in \mathbb{Z} \}$, $A$ is a subset of $S$, satisfying $\operatorname{card}(A) = p$ $\sum\limits_{x\in A} x \equiv 0 \pmod p$...
122 views

### Iterative calculation of a number-theoretical constant [closed]

Recently the decimal expansion of a number theoretic constant was searched for, which is the analog of the Landau-Ramanujan constant in a certain context. The constant starts 0.638909... It can be ...
98 views

### Finding minimum x such that Mod[3^x, m] == 1 for m not multiple of 3 [closed]

I would like to find smallest x value for each m value such that Mod[3^x, m] == 1, where m is not multiple of 3. Here is my ...
I created a list with all divisors of 18000: list1 = Divisors[18000] I did an analysis to identify which of these numbers are divisible by $15$, but the result I ...