# Questions tagged [modular-arithmetic]

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### Adding Points on an Elliptic Curve

How do I do this in Mathematica? The curve given by the equation $y^2 = x^3 + 29x + 7$ defined over the integers modulo $10007$ Adding the first pair of points $P = (3737, 4549)$ and $Q = (8286, 6097)$...
1 vote
51 views

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### Command to find the pre-image of a set that is mapped to by the function $f(x)=3^x \mod{17}$

$$f(x)=3^x \mod{17}$$ How to find the pre-image of the set if this function maps from real numbers to real numbers. What command would I use, to see the pre-image if the function would map from ...
309 views

### Plot solution to damped driven pendulum in $(-\pi,\pi)$

I'm solving the damped driven pendulum: ...
84 views

### Modulus option quietly nerfed for Solve?

Recently asked my students to put together something like this: Reduce[x^2 ==b, b, Modulus -> 11] For me, on 12.1, this gives: ...
81 views

### PowerMod solve for b (exponent)

Using PowerMod[a, b, m] = x I get ...
466 views

### How to ask Mathematica to solve a simple modular equation

What's the most straightforward way to ask Mathematica to find all solutions of an equation like $$3x + 2y + 4z = 0 \pmod {11}$$ (for instance), where either $x$, $y$, $z$ can be considered to be ...
75 views

### Can Mathematica automatically optimize an expression with PowerMod?

PowerMod[x,p,m] is significantly faster than Mod[x^p, m] for a large p I have an expression, ...
1 vote
78 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 ...
48 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 ...
81 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: ...
216 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 ...
2k 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) $\bmod n$...
80 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
63 views

### How to apply PolynomialMod to a SparseArray?

I have a list bdrs of SparseArrays, whose entries are polynomials in the variable t with ...
54 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 <...
120 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 ...
67 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 ...
816 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 }
677 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 ...
157 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
385 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 ...
257 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
78 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 ...
390 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 ...
50 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{}? ...
255 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 ...
791 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 ...
174 views

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

I have the following $2$-dimensional implicitly defined map ...
1 vote
144 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 ...