Number Theory Algorithms

Description of Number Theory Algorithms

Calculator:
Add two big integer numbers
Subtract two big integer numbers
Multiply two big integer numbers
Divide two big integer numbers
Power of a big integer number
Root of a big integer number
Greatest Common Divisor (GCD) of two big integer numbers
Lowest Common Multiple (LCM) of two big integer numbers
Modulo of two big integer numbers
Modulo Inverse of two big integer numbers
Check if a big integer is probable prime
Euler's phi-function
Factorial
Next probable prime to a big integer number
Next twin prime pair to a big integer number
Algorithms:
Simple Quadratic Form. Solve for x,y such as bxy dx ey=f where b,d,e,f,x,y in Z.
Euclidean Algorithm. Compute the Greatest Common Divisor (GCD) of two numbers a and b.
Extended Euclidean Algorithm. Solve for x, y such as ax by = gcd(a, b).
Linear Diophantine Equation In Two Variables. Solve for x,y such as ax by=c.
Linear Congruence In One Variable. Solve for x a congruence of the form ax ≡ b (mod m).
Linear Congruence In Two Variables. Solve for x,y a congruence of the form ax by ≡ c (mod m).
Tonelli-Shanks Algorithm. Calculate the Quadratic Residue Modulo. Solve for x, a congruence of the form x² ≡ a (mod p) where p is prime.
Mod Factors. Calculate modular possible factors for a given number and a modulo. Find n ≡ bc (mod a) where (ax c)(ay b) = a(axy bx cy) bc = n.
Primes List. List of primes ordered in columns.
Note: Performance is based on the device.