# Questions tagged [number-theory]

Questions on the number-theoretic functionality of Mathematica.

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### Multiplicative partition function

I am trying to create a multiplicative partition function that would generate something like ...
487 views

### Implementing Kane's Subset Sum Algorithm

In the following paper, D. Kane describes an algorithm for subset sum that runs in logspace: http://arxiv.org/pdf/1012.1336v2.pdf. I am trying to implement it ...
268 views

### Solving Thue equations

A Thue equation is a 2-variable homogeneous integer polynomial of degree at least 3. It's well-known that such equations have only finitely many solutions over the integers. I'm trying to solve some ...
377 views

### Conveying density of 5-smooth (Hamming) numbers

A number is 5-smooth if its only prime factors are 2, 3 or 5. Example: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, … Interesting thing is that as they become larger and ...
378 views

### Is there a PrimeQ whose accuracy guarantee you can adjust?

Say I have a list of a million integers each with a million digits, and I want a crude sieve to see which have a chance at being prime. Mathematica has a PrimeQ function, which appears to be slow ...
167 views

### Testing the Erdos square free conjecture

Can someone please answer these two parts of my homework assignment? Adding an explanation would be appreciated! a. Test the Erdos square free conjecture for $n <= 30000$. You should use ...
125 views

### Approximate to the speed of Built-In functions

In Mathematica, there is a function PowerMod[a,b,m], which computes a^b mod m. I will concern only this case: ...
1k views

### Elliptic curve cryptography in Mathematica

I can find no resources for doing elliptic curve cryptography. I have used the finite field package, but I find it cumbersome and it does not seem to have any builtin methods for ECC. How can I get ...
212 views

### Square root of a value defined in a finite field?

I am trying to find the right way to compute the square root of a number defined in a finite field. For example, ...
645 views

### Why is my solution to PE #5 so slow

I'm new to Mathematica and it was suggested to me to go through the Project Euler problems in order to learn it. However, I can't quite figure out why my solution to #5 is so slow. The problem: ...
139 views

Going through Derbyshire's Prime Obsession & trying to take LogIntegral of 20^ZetaZero & comes up with a value of <...
231 views

### How to calculate the residue of $1/f(z)$ at a numerical approximation to a root of $f(z)$?

The input Residue[1/DirichletL[19,10,s],{s,s0}] gives 0 even when s0 is a root. For ...