Number Theory Apps

GcdTab

Table of greatest common divisors

SimpleEuAlgDem

Simple Euclidean algorithm step by step

EuAlgDem

Advanced Euclidean algorithm demonstration

LnComTab

Table of integral linear combinations

Factor

Canonical factorization into prime powers

FacTab

Table of least prime divisors

SieveOfEratosthenes

Visual demonstration of the sieve

GetNextP

Finds the next prime number

Pi

Counts the primes not exceeding x

SPsP

Runs the strong pseudoprime test

SPsPDem

Strong pseudoprime test step by step

ProveP

Proves that a given number is prime

CngArTab

Modular addition and multiplication tables

LinCon

Solves linear congruences

CRT

Chinese Remainder Theorem calculator

IntApTab

Intersection of arithmetic progressions

PascalsT

Pascal’s triangle modulo n

PolySolv

Solutions of a polynomial modulo n

Power

Computes a power modulo n

PwrDem

Modular exponentiation step by step

FctrlTab

Table of factorials modulo n

Order

Multiplicative order calculator

OrderDem

Multiplicative order step by step

PowerTab

Table of powers modulo n

PrimRoot

Finds a primitive root modulo p

IndTab

Indices and powers for a primitive root

Ind

Discrete logarithm using Shanks’ method

IndDem

Shanks’ algorithm step by step

Phi

Euler’s totient function calculator

Car

Carmichael function calculator

P–1

Pollard’s p − 1 factorization method

P–1Dem

Pollard’s p − 1 method step by step

Rho

Pollard’s rho factorization method

RhoDem

Pollard’s rho method step by step

Jacobi

Jacobi symbol calculator

JacobDem

Jacobi symbol step by step

JacobTab

Table of Jacobi symbols

SqrtModP

Square root modulo p calculator

SqrtDem

Square roots modulo p step by step

QFormTab

Quadratic forms with a given discriminant

Reduce

Reduces a binary quadratic form

ClaNoTab

Displays a table of class numbers

QuadraticPowerTab

Powers of a + b√d

QuadraticRingElements

Elements of ℤ[√d], their norms and irreducibility

QuadraticRingFactorization

Decompositions of numbers in ℤ[√d]

ContinuedFraction

Continued fraction of a + b√d

PCFEvaluator

Evaluates a periodic continued fraction

ArFcnTab

Table of six arithmetic functions

FFArTab

Finite-field arithmetic tables

Hensel

Executes the Hensel lifting procedure

HSortDem

Demonstrates the HeapSort algorithm

PolynomialDiscriminant

Discriminant of a polynomial

RSA

Encrypts and decrypts messages using RSA

SumsPwrs

Writes n as a sum of powers