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Dihedral group D4 composition with custom labels

The dihedral group $D_4$ is the symmetry group of the square, that is the moves that transform a square to itself via rotations and reflections. It consists of 8 elements: rotations by 0, 90, 180, ...
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Fundamental Solution of the Pell Equation

Given some positive integer $n$ that is not a square, find the fundamental solution $(x,y)$ of the associated Pell equation $$x^2 - n\cdot y^2 = 1$$ Details The fundamental $(x,y)$ is a pair ...
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Order of Elements of the Rubik's Cube [duplicate]

Introduction All the possible moves and their combinations of a Rubik's Cube form a group. A group in general is a set with some binary operation defined on it. It must contain a neutral element with ...
309 views

Finite Field Multiplication

Overview Given the integer representation of three elements in GF(2^64), give the product of the first two elements over GF(2^64) with the reducing polynomial defined as the polynomial m such that m(...
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Decompose Polynomials

Given an integral polynomial of degree strictly greater than one, completely decompose it into a composition of integral polynomials of degree strictly greater than one. Details An integral ...
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Sparse Protractor

Given some positive integer n, design a protractor with the fewest number of marks that lets you measure all angles that are an integral multiple of ...
286 views

Counting Moufang Loops

A loop is a pretty simple algebraic structure. It is a tuple (G,+) where G is a set and + is a binary operator G × G → G. That is + takes two elements from G and returns a new element. The operator ...
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Determine How many Wheels There Are

Non-math explanation This is an explanation that is meant to be approachable regardless of your background. It does unfortunately involve some math, but should be understandable to most people with a ...
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(-a) × (-a) = a × a

We all know that (-a) × (-a) = a × a (hopefully), but can you prove it? Your task is to prove this fact using the ring axioms. What are the ring axioms? The ring axioms are a list of rules that two ...
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Group Therapy: Identify Groups

Write a program, that determines whether the multiplication table of the given finite magma represents a group. A magma is a set with a binary operation that is closed, that means for all a,b in G, a*...
830 views

Factor a polynomial over a finite field or the integers

Without using any built-in factoring/polynomial functions, factor a polynomial completely into irreducibles over the integers or a finite field. Input Your program/function will receive some prime (...
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Generate the group table for Z_n

Groups are a widely used structure in Mathematics, and have applications in Computer Science. This code challenge is about the fewest # of characters to create a group table for the additive group Zn. ...