Number Theory
Prime factorization, modular arithmetic, CRT, Euler totient, Fibonacci, perfect numbers, continued fractions, Diophantine equations, bases, and divisibility.
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Chinese Remainder Theorem Calculator
Solve systems of congruences using the Chinese Remainder Theorem. Find x such that x ≡ r1 (mod m1) and x ≡ r2 (mod m2).
Continued Fraction Calculator
Convert a fraction to its continued fraction representation. Shows coefficients, convergents, and approximation error.
Diophantine Equation Calculator
Solve linear Diophantine equations of the form ax + by = c. Find integer solutions using the Extended Euclidean Algorithm.
Divisibility Calculator
Check if one number divides another. Shows remainder, quotient, and total factor pair count.
Euler's Totient Calculator
Calculate Euler's totient function phi(n) — the count of integers from 1 to n that are coprime to n.
Fibonacci Calculator
Calculate the nth Fibonacci number, its predecessor, and the golden ratio approximation F(n)/F(n-1).
Modular Arithmetic Calculator
Perform modular addition, multiplication, and exponentiation. Calculate (a op b) mod m with equivalence classes.
Number Base Converter
Convert numbers between any base (2-36). Enter a number in one base and convert to another.
Perfect Number Calculator
Check if a number is perfect, abundant, or deficient by computing the sum of its proper divisors.
Prime Factorization Calculator
Find the complete prime factorization of any number up to 1,000,000. Shows all prime factors, exponents, and primality.