# Tagged Questions

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### Inverse of a polynomial in a polynomial ring

Let $N$ be a prime, and $q$ be a positive integer. Given a polynomial $f(x)$ in $R = \mathbb Z[x]/(x^N-1)$, I want to find another polynomial $f_q(x)$ in $R_q = \mathbb Z_q[x]/(x^N-1)$, such that f(...
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### Solving/Reducing equations in $\mathbb{Z}/p\mathbb{Z}$

I was trying to find all the numbers $n$ for which $2^n=n\mod 10^k$ using Mathematica. My first try: Reduce[2^n == n, n, Modulus -> 100] However, I receive ...
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### Montgomery Modular Exponentiation

I'm trying to write a Montgomery exponentiation based on this which can compete with Mathematica PowerMod. We know that PowerMod ...
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### Linear Solve with Modular Arithmetic

I am interested in using LinearSolve[m,b] which will find a solution to the equation $m.x=b$, where I am in mod 2 arithmetic. Is there any way to perform this ...
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### How can I seperate specific elements from the list? [duplicate]

Possible Duplicate: Question about MapThread and Dynamic I write a function name as inputFieldsList and it returns both ...
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### Implementing Remainder Tree

I want to implement Remainder Tree based on this. With the answers on SE I've come up with: ...
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### Parallel PowerMod

Is there anyway to parallelize the PowerMod function? Here is my Left-To-Right modular exponentation: ...
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### Incrementing a number where each digit has a different base

Let's say I have a list, for instance {10,5,3}, indicating the bases for each digit of my 3-digit number. Using this basis, if I wanted to increment {8,4,1} a couple of times, here's what I would get: ...
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### Matrix Multiplication Modulo 2

I would like to perform matrix multiplication modulo 2. Hence, instead of the usual: A.B I did: ...
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### decompose a number (less than 255) in a sum of powers of 2

Is there a built in function that would take a number and decompose it into a sum of powers of 2? The numbers will be non negative less than 256. For what it's worth I'm trying to understand a paper ...
### Factorizing polynomials over fields other than $\mathbb{C}$
I'd like to take a polynomial in $\mathbb{Z}_5[x]$ of the form $ax^2+bx+c$ and factor it into irreducible polynomials. For example: Input... x^2+4 Output... <...