Number Theory Calculators
Last updated: October 2026
Pythagorean Triples Generator
Generates all Pythagorean triples (a, b, c) satisfying a² + b² = c² up to a chosen limit, classifying each as primitive or non-primitive.
Quadratic Residue Calculator
Determine whether an integer a is a quadratic residue modulo a prime p, and compute the Legendre symbol (a/p).
Perfect Number Analyzer
Check whether a number is perfect, abundant, or deficient by comparing it to the sum of its proper divisors.
Divisor Count Calculator
Count exactly how many divisors a positive integer has, including 1 and itself.
Linear Diophantine Equation Solver
Finds all integer solutions to a linear Diophantine equation of the form ax + by = c.
Binary to Decimal Converter
Convert any binary (base-2) number to its decimal (base-10) equivalent in one click.
Fibonacci Sequence Calculator
Generates Fibonacci sequences with custom starting values and computes the nth term or cumulative sum using Binet's formula.
Divisibility Test Calculator
Test whether a specific number is divisible by a chosen divisor, or count all divisors up to a custom limit.
Modular Arithmetic Calculator
Computes modular addition, multiplication, and exponentiation of integers under a chosen modulus.
Collatz Conjecture Analyzer
Trace the Collatz sequence from any starting integer — halving evens and applying 3n+1 to odds — until reaching 1.
Pascal's Triangle Calculator
Generate rows of Pascal's triangle or look up any individual binomial coefficient C(n, k).
Prime Gap Analyzer
Scans a user-defined range of integers, identifies all primes, and computes the gaps between consecutive primes including maximum, minimum, and average gap.
Factorial Calculator
Calculates n!, the product of all whole numbers from 1 to n, for n from 0 to 169, and explains how factorials count arrangements and combinations.