# Number Theory

1. Alpertron
2. Number Theory

This site features:

1. Generic Two integer variable equation solver: Diophantine equation ax2 + bxy + cy2 + dx + ey + f = 0 solver, where the unknowns x and y can be integer numbers only.

2. Quadratic modular equation solver: Calculator that can solve equations of the form ax2 + bx + c = 0 (mod n).

3. Sum of powers: Table of relations of the form ap + bq = cr with gcd(a,b,c) = 1.

4. Ulam's Spiral: Web application featuring a graphical view of prime numbers.

5. 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.

6. 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.

7. Gaussian Primes: Web application featuring a graphical view of gaussian prime numbers.

8. Discrete logarithm calculator: Web application that finds the exponent in the expression BaseExponent = Power (mod Modulus).

9. Continued fraction calculator: This calculator can find the continued fraction expansions of rational numbers and quadratic irrationalities.

10. Every positive integer is a sum of four integer squares: Constructive proof of this interesting theorem.

11. 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.

12. 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.

13. Brilliant numbers: Interesting problem about products of primes of the same size.

14. Factors of Modified Fermat Numbers: Factors of numbers of the form 43n+23n+1 and 43n-23n+1.

15. Factors of numbers near googolplex (1010^100):

• Table 1: Factors of numbers in the range 1010^100 to 1010^100 + 999.

• Table 2: Factors of numbers in the range 1010^100 - 999 to 1010^100.

• Table 3: Factors of numbers of the form 1010^100 + 10Exp, where 0 <= Exp <= 9.

16. Factors of numbers near googolplexplex (10googolplex):

• Table 1: Factors of numbers in the range 1010^(10^100) to 1010^(10^100) + 999.

• Table 2: Factors of numbers in the range 1010^(10^100) - 999 to 1010^(10^100). Cool math site of the week
August 30th, 2002.