12月17日 的 Number Theory Algorithms 應用程式分析

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 Module of two big integer numbers Module Inverse of two big integer numbers Module Power Check if a big integer is prime Euler's phi-function Factorial Next prime to a big integer number Next twin prime pair to a big integer number Algorithms: Simple Quadratic Form. Solve for x,y such that 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 that ax + by = gcd(a, b). Linear Diophantine Equation In Two Variables. Solve for x,y such that 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 modulus. 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.