Number Theory Algorithms

ERVIN GEGPRIFTI

About this app

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.

What’s new

- Added compact input view mode.
- Added a temporary field in the calculator for intermediate result storage.
- Added input decrease (-) increase (+) buttons.
- Added a double-tap event on the result to expand it, despite the expand button.
- Added results history in the calculator.
- Added modular power in the calculator.
- Unified vibration on button tap.
- Removed the notify on button tap since buttons them-self indicate that.
- Refactored part of the code.