Questions tagged [modular-arithmetic]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1
vote
1answer
51 views

A modular version of LinearRecurrence?

I'm playing around with implementing the Lucas probable prime test (mainly so I can understand it better), and would love a version of the LinearRecurrence function that used addition modulo n (with n ...
0
votes
1answer
41 views

Find relationship between values within finate range of integer domain

Update: There are some misakes in the coefficient of left and right. But still get similar result. I understand the mathematica ...
2
votes
1answer
40 views

How to simplify quotient and mod in integer domain

I want to simplify (a*32 + a%32)/32, and a is integer. So I write: ...
2
votes
1answer
45 views

Non-valid modulus when using LinearSolve

I have a system of linear equations I want to solve mod 4, and I happen to know the solution, but I get an error when trying to solve it using LinearSolve. I define the matrix ...
11
votes
3answers
1k views

How can I program the last digits of Fibonacci numbers?

Is there a way to compute the last digits of an arbitrarily large Fibonacci number? For the $10^n$th Fibonacci number, we can just find the $2^n$-th Fibonacci number (if that isn't too large) $\bmod n$...
2
votes
1answer
54 views

How to get the modulus of two functions [closed]

I might be overlooking something, because what I want to do is quite elementary. I want the following term Mod[2(1 + z), (1 + z)] to evaluate to ...
1
vote
0answers
54 views

How to apply PolynomialMod to a SparseArray?

I have a list bdrs of SparseArrays, whose entries are polynomials in the variable t with ...
2
votes
0answers
40 views

Why gives Modulo of complex numbers different answers for rationals and reals

When running Table[1.*Mod[(1 + I)^(1 + k*I), 1 + k*I], {k, 49, 50, 0.5}] Table[1.*Mod[(1 + I)^(1 + k*I), 1 + k*I], {k, 49, 50, 1/2}] I get for the first table <...
4
votes
3answers
106 views

how can I calculate $a_{n+3}=a_n+a_{n+1}+a_{n+2}$?

recently I need to calculate this: $a(n+1)=((a(n-2)+a(n-1)+a(n)) \bmod 10000)$ and get $a(20000000)$ (for example). I know RecurrenceTable,but ...
0
votes
0answers
50 views

Finding a solution to a modular problem efficiently

I want to find a naïve hash function of the form Mod[a x + b, 2^p] which would produce a value less or equal to v for all ...
5
votes
1answer
627 views

modulo with n instead of 0 without using if-statement

Is there a way to to express the following without using an if statement, but with mathematical operations instead? { 5 if x % 5 = 0, x % 5 otherwise }
2
votes
1answer
221 views

How to Plot modulo function Mod on a function of two variables? [closed]

I know that Plot[Mod[x, 2], {x, -6, 6}] is a Mathematica command to plot the remainder of x over 2 when I range x over reals -6 to 6. How do I plot the same ...
5
votes
1answer
95 views

FindEquationalProof to prove divisor theorem

I'm trying to implement proofs of concepts for Equational Proofs on some basic number theory theorems. One such example is: "let a and b be positive integers and let d = gcd (a, b). If t divides ...
1
vote
1answer
173 views

Polynomial PowerMod

Is there equivalent of PowerMod for polynomials in Mathematica? We have Mod[a^e,m]==PowerMod[a,e,m], $a$, $e$ and $m$ all ...
3
votes
1answer
108 views

List of invertible congruence classes

I am attempting to create a list of the invertible congruence classes $\bmod 120$. The code I have is ...
1
vote
1answer
67 views

Is this decryption function idiomatic?

This is my first non-trivial Mathematica notebook, which I wrote for a cryptology homework. It encrypts/decrypts strings using an affine cipher. Is the code readable/idiomatic? How could it be ...
4
votes
3answers
347 views

How to reverse in modular arithmetic

Given an RGB color {127, 255, 212} where scale is 0-255, VBA's RGB function find a long integer x such that ...
0
votes
1answer
43 views

Looping on ranges (Modular iterations)

Is it possible to make the following code modular, so that it works up till depth n, and returns an array of all possible combinations for used{}? ...
2
votes
1answer
134 views

How to solve a system with GCD?

For example, Solve[{x + y == 150, GCD[x, y] == 30}, {x, y}, Integers] Solve::nsmet: This system cannot be solved with the methods available to Solve. The same ...
6
votes
1answer
308 views

RowReduce modulo 3

When I wanted to compute a row echelon form of a matrix over the finite field ${\Bbb F}_9$ with 9 elements (which is the three element field ${\Bbb F}_3$ adjoined a square root of $-1$ which I denote ...
0
votes
0answers
102 views

Variables defined modulo $\pi$ and avoiding singularities; phase plotting for a map

I have the following $2$-dimensional implicitly defined map ...
1
vote
1answer
114 views

Solving a modular equation with a large modulus [duplicate]

I am having trouble solving this equation: $17^n\equiv 1 \mod 640826899755722841329632946651705039010285107743541637238400825304943424424715705661705191669759$ for the smallest integer $n > 0$ I ...
0
votes
1answer
50 views

Get missing cyclic numbers via modulus?

Consider a list of numbers: list = {1,2,3,4,5}; Taking a random set of three of these numbers: ...
7
votes
2answers
1k views

How can I solve a certain congruence equation?

I want to solve the congruence $3x^2 + 6x + 1 \equiv 0 \pmod {19}$. I know that one way to solve this is to first solve the congruence: $t^2 \equiv 5 \pmod {19}$, because $b^2 - 4ac \equiv 24 \equiv ...
4
votes
1answer
223 views

Matrix operations “Modulus->non-prime” problem

I am using Mathematica 10.4.1.0. When I specify the "Modulus" option to be a non-prime, the functions RowReduce and MatrixRank return the error ...
2
votes
1answer
161 views

How to remove symmetries from this list?

First of all, I work with modular arithmetics and the elements of the arithmetics are lists themselves. I recognize two kinds of symmetries - shift and mirroring. We could define shift of a list like ...
9
votes
1answer
171 views

Modular equation problem

I have problem solving this modular equation $67^n \equiv 67 \pmod {317026939759222841944}$ with $n>1$. I have tried my Laptop and Wolfram Alpha engine, but I don't get any solution, I'm very ...
1
vote
0answers
69 views

Last digits via PowerMod [closed]

Do you have an idea why this produces different results? PowerMod[2003, 2002^2001, 1000] 241 ...
6
votes
2answers
199 views

Memory problem when solving a system of modular equations [duplicate]

I need to solve the following system of modular equations, but the computation can't finish because I run out of memory (I have 12 GB of RAM). Is there any workaround to this problem? I am using ...
0
votes
0answers
53 views

Function to add two matrices mod 2 [duplicate]

I have: lightstep[m_, gg_] := Which[gg == {1, 1}, m = Mod[m + m, 2]] Then I entered: A = {{1, 1, 0}, {1, 0, 0}, {0, 0, 0}} ...
2
votes
0answers
90 views

Finite fields package doesn't simplify

I'm trying to do arithmetic using the FiniteFields package. Supposing a is a generator of a Galois field (say GF(2^5)) I want to be able to simplify things like a^32 and (a^8)^-1. I don't care about ...
0
votes
1answer
58 views

Putting some calculations together to form an algorithm

Considering these below where n is an odd number, k is also an odd number less than n: <...
3
votes
1answer
192 views

Coppersmith method of small integer solutions to multivariate polynomials

In http://link.springer.com/chapter/10.1007%2F3-540-68339-9_14#page-7 is presented a method for finding small solutions to multivariate polynomials. (Although here he mentions that it "is not rigorous"...
3
votes
2answers
307 views

Evaluate modular fractions

If I have a list of numbers l = {256/11, 258/11, 263/11, 263/11, -22, -22, 251/11, 0, 261/11, -22, 265/11, 259/11, 0, 259/11} which I want to evaluate mod 26, how ...
-2
votes
1answer
72 views

Want code for a modular operation

Given numbers a1 and a2 and a positive integer k, such that ...
11
votes
2answers
760 views

MatrixPower with Modulus

I have a matrix that will be multiplied with itself by an extremely large amount of times under $Z/pZ$. The matrix itself contains small numbers, so ...
4
votes
0answers
160 views

Sparse matrix multiplication mod p

Let A and B be sparse matrices with integer coefficients between 0 and ...
2
votes
1answer
323 views

Get Mathematica to solve Modular Arithmetic problem [closed]

How would I get Mathematica to solve something like this for $x$? $4x \equiv 1 \pmod 5$
2
votes
0answers
122 views

What does Mod^(1,0) mean in mathematica output [closed]

I am trying to take he derivative of mod(remainder). In:= D[Mod[x, y], x] Out = Mod^(1,0)[x,y] I cannot understand the meaning of Mod^(1,0). What does the ...
-1
votes
3answers
119 views

Create table of elements which belongs to specific sets

I would like to produce elements (preferably by Table or For-If commands) that they belong to specific sets. For example I want to write positive integers from 1 to 100 such that they are $2 \pmod 3$, ...
2
votes
1answer
92 views

A Difficult Application of Modular Arithmetic

Looking to input a $p$ for the first line: p=6; Build a list of primes from the 3rd to $p-1$: ...
2
votes
1answer
143 views

Twin Prime Max Gaps (Performance Tuning)

Ok, let's build a foundation here: A common way of testing primality, is dividing by all primes smaller than the number's square root. For instance, $97$ is prime because dividing by none of the ...
3
votes
2answers
123 views

Using “Outer” with “ChineseRemainder”?

I'm looking to build a $7\times3$ matrix using ChineseRemainder. Trying to use ${0,1,2,3,4,5,6} \pmod 7$ and ${3,15,21} \pmod {30}$ so that the first element of ...
8
votes
1answer
288 views

Taking one list Mod a second list

Just on my free trial and can't find this anywhere in online docs. Trying to use the Mod function as follows: Mod[{list},{list}} where it takes each number in list ...
8
votes
1answer
149 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 <...
1
vote
1answer
86 views

Simplify Mod to subtraction when possible

FullSimplify[Mod[t,10], t>101 && t<109] It's a long shot, but can I get Mathematica to return t-100 or something ...
27
votes
1answer
2k views

Fast calculation of discrete logarithms

Does Mathematica have any built-in fast algorithms for calculating discrete logarithms over $(\mathbb{Z}_p)^\times$ (the group of integers modulo $p$)? Essentially, for a fixed large prime ...
2
votes
0answers
80 views

Sum of zeros in finite Galois field

In the following code: << FiniteFields` GF[2][{0}] + GF[2][{0}] == GF[2][{0}] GF[2][{0}] + GF[2][{0}] + GF[2][{0}] == GF[2][{0}] Why does the second line ...
1
vote
1answer
76 views

What is the correct idiom for mapping a 0 value in a modulo n expression back to n?

What is the correct idiom for mapping the $0$ value in a modulo $n$ expression back to $n$. For example if I want to be sure that any integer value maps back to the index for a character in the ...
2
votes
2answers
10k views

Check RUT (Rol Único Tributario) for numbers over 7 digits

In Chile the RUT (Rol Único Tributario) is a national identification number. Every RUT has a check digit modulo 11. The RUT has 7 or 8 digits plus a check digit or letter. I made this code that works ...