# Web applications written by Dario Alpern

- Alpertron
- Web applications

The programs in this site are:

**Generic Two integer variable equation solver:**Diophantine equation**ax**solver, where the unknowns^{2}+ bxy + cy^{2}+ dx + ey + f = 0**x**and**y**can be integer numbers only. Written in Java/JavaScript. Now it includes source code.**Quadratic modular equation solver:**Calculator that can solve equations of the form**ax**.^{2}+ bx + c = 0 (mod n)**Ulam's Spiral:**This program features a graphical view of prime numbers.**Factorization using the Elliptic Curve Method:**Application that can be used to find 20- or 30-digit (or more if it runs longer) factors of numbers or numerical expressions up to 100000 digits long. It also computes the number and sum of divisors, Euler's totient and Moebius, and its decomposition as a sum of up to 4 perfect squares.**Gaussian Integer Factorization applet:**It finds the factors of complex numbers of the form a+bi where a and b are integers. It also includes a complete calculator with operators and functions using gaussian integers.**Gaussian Primes:**This program features a graphical view of gaussian prime numbers.**Discrete logarithm calculator:**It finds the exponent in the expression`Base`^{Exponent}=`Power`(mod`Modulus`).**Continued fraction calculator:**This calculator can find the continued fraction expansions of rational numbers and quadratic irrationalities.**Sum of squares:**This calculator can find the decomposition of a number or numerical expression in a sum of up to four squares. It does not need its prime factorization.**Polynomial factorization:**This calculator can find the decomposition of an integer polynomial or a polynomial modulo a prime in a product of irreducible factors. In the first case it also shows the exact roots using radical expressions.**Distance between cities**:It has a database of 105 cities, with their geographic locations. You can get the distance between any two cities of the database.

The program contains two tests. In the first the user must input the distance between two random cities given by the computer (there are ten questions). In the second test there are a departure city, a destination city, and four more. The user should minimize the distance traveled by passing through the six cities.

Press here to run the program

Press here to obtain the source code