- Alpertron
- Number Theory

This site features:

**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.**Quadratic modular equation solver:**Calculator that can solve equations of the form**ax**.^{2}+ bx + c = 0 (mod n)**Sum of powers:**Table of relations of the form**a**with^{p}+ b^{q}= c^{r}**gcd(a,b,c) = 1**.**Ulam's Spiral:**Web application featuring a graphical view of prime numbers.**Factorization using the Elliptic Curve Method:**Web application that can be used to find 20- or 30-digit factors of numbers or numerical expressions up to 1000 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 calculator:**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:**Web application featuring a graphical view of gaussian prime numbers.**Discrete logarithm calculator:**Web application that 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.**Every positive integer is a sum of four integer squares:**Constructive proof of this interesting theorem.**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.**Sum of four cubes:**This calculator can find the decomposition of a number or numerical expression that is not congruent to 4 or 5 (mod 9) in a sum of four cubes.**Brilliant numbers:**Interesting problem about products of primes of the same size.**Factors of Modified Fermat Numbers:**Factors of numbers of the form 4^{3n}+2^{3n}+1 and 4^{3n}-2^{3n}+1.**Factors of numbers near googolplex (10**:^{10^100})**Factors of numbers near googolplexplex (10**:^{googolplex})