# Questions tagged [number-theory]

Questions on the number-theoretic functionality of Mathematica.

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### Identifying repeating patterns in a list of numbers

I have some generated lists of natural numbers which have a small number of distinct values, ie. referencing the variable "rowToCheck" for each list: list1: rowToCheck = 3: length=7, distinctvalues=3 ...
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### Is there a function or a way of getting a remainder or modulus with equations with “surds”?

So I'm working with "surds", or radicals. I have expressions like $$7 + 5\sqrt{2} + 6\sqrt{3} + 7\sqrt{6}\tag{1}$$ and I want to take the "coefficients", for lack of a better word, and take their ...
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### Finding the maximal number of lists that form certain rules?

I have the following example: data={1, 2, 3, 4, 5, 6, 7, 8, 9}; NN=Length[data]/3; subdata=Subsets[data, {3}]; I want to know all the possibility for the ...
389 views

### Drawing a sequence of circles

For every natural number from 1 to 150, draw a circle centered on the x-axis in that number and with the diameter equal to the number of divisors of the number. I don't know what should I do.
184 views

### solve for two variables for each n related to Collatz conjecture

For this code, for each x I would like to solve for all value ranges for c1 and c2 in a bounded range ie c1 and c2 in the range of real numbers +-100 for c1 and c2 for each x, which combined give "...
174 views

### automatic formula finding function [duplicate]

I am curious how easy it would be to automatically find some formulas related to basic number theory OEIS sequences using some Mathematica search algorithm for a small set of OEIS sequences as a ...
43 views

### 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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869 views

### 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[]"...
327 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): ...
151 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 ...
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### 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 ...
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### 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 d ...
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### 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 ...
463 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?
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### 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 ...
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### FunctionDomain in the Reals numbers [closed]

Why don't I obtain that $x$ belongs to the Reals? ...
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### 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 ...
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### 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 ...
325 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 ...
54 views

### 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/Sqrt[2 + Sqrt] * 2/Sqrt[2 + Sqrt[2 + Sqrt]] * ... ...
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### Question about using ParallelMap to speed up computations [duplicate]

First; I define two functions: ...
### 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?
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 ...