# Tagged Questions

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746 views

### 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 ...
731 views

### 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... <...
289 views

### Mod[1.2, 0.2] is not equal to zero

Why doesn't the following expression evaluate to zero? In[1]:=Mod[1.2, 0.2] Out[1]=0.2 Edit: This is what I wanted to do: ...
295 views

### Parallel PowerMod

Is there anyway to parallelize the PowerMod function? Here is my Left-To-Right modular exponentation: ...
3k views

### Solving a system of linear equations modulo n

I have a system of linear equations $$a+b+c \equiv 31 \pmod{54}$$ $$4a+2b+c \equiv 3 \pmod{54}$$ $$9a+3b+c \equiv 11 \pmod{54}$$ What should I input (I'm using ...
104 views

### Bug in PiecewiseExpand and Mod with assumptions

Bug introduced in 9.0 or earlier and fixed in 10.4 The following code using PiecewiseExpandand Modgives the wrong answer <...
921 views

### How to Simplify equations over a Ring with Mathematica?

For example, when we work over a ring, the equation x^3=0 does not imply x^2=0 or x=0, but ...
1k views

### 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(...
915 views

### 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 ...