Advanced Math Tools
A collection of advanced mathematical calculators and utilities for number theory, combinatorics, sequences, and more.
Number Theory
Tools for exploring prime numbers, divisibility, modular arithmetic, and the fundamental properties of integers.
Check if a number is prime with an efficient algorithm.
Decompose any positive integer into its prime factors with step-by-step explanation.
Calculate φ(n) - the count of integers from 1 to n that are coprime to n.
Calculate τ(n) and σ(n) - the count and sum of all divisors of a positive integer.
Find the GCD and Bézout coefficients of two numbers.
Calculate a^b mod m efficiently using binary exponentiation.
Solve systems of linear congruences with step-by-step solutions.
Calculate μ(n) - a fundamental function in number theory used in the Mobius inversion formula.
Combinatorics
Counting, arrangements, partitions, and the mathematics of discrete structures.
Calculate nPr and nCr with large number support.
Calculate D(n) - the number of permutations where no element appears in its original position.
Expand (a + b)^n using the binomial theorem with step-by-step coefficients.
Calculate the number of ways to partition a positive integer into sums of positive integers.
Generate and count Dyck paths for combinatorial analysis.
Calculate r₅(n) - the number of ways to represent n as a sum of five squares.
Calculate Stirling numbers of the first and second kind for counting permutations with cycles and set partitions.
Calculate Catalan numbers that count balanced parentheses, binary trees, and many other combinatorial structures.
Sequences
Explore famous sequences, iterative processes, and convergent series.
Calculate Fibonacci numbers and explore the golden ratio.
Explore the famous 3n+1 problem by generating Collatz sequences and analyzing their behavior.
Convert numbers to continued fraction representation and compute convergents.
Algebra
Solve equations, work with polynomials, and convert between number systems.
Geometry
Calculate areas, visualize curves, and work with geometric shapes.
Linear Algebra
Matrix operations and transformations for vectors and linear systems.
Numerical Methods
Approximation techniques, simulations, and computational approaches to mathematical problems.