Articles and calculators about Number Theory

1. Alpertron
2. Number Theory articles and calculators

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 a^p + b^q = c^r 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 Base^Exponent = 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. Sum of two squares and a power: This calculator can find the decomposition of a number or numerical expression that in a sum of two sqaures and a cube, fifth or seventh power.

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

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

16. Factors of numbers near googolplex (10^{10^100}):

    • Table 1: Factors of 1000 numbers starting from googolplex: range 10^{10^100} to 10^{10^100} + 999.

    • Table 2: Factors of 1000 numbers up to googolplex: range 10^{10^100} − 999 to 10^{10^100}.

    • Table 3: Factors of googleplex plus powers of 10, this is, numbers of the form 10^{10^100} + 10^Exp, where 0 <= Exp <= 9.

    • Table 4: Known factors of googolplex minus 1, that is, 10^{10^100} − 1.

    • Table 5: Known factors of googolplex minus 10, that is, 10^{10^100} − 10.

    • Table 6: Known factors of googolplex plus 10, that is, 10^{10^100} + 10.

17. Factors of numbers near googolduplex (10^googolplex):

    • Table 1: Factors of 1000 números starting from googolduplex: range 10^{10^(10^100)} to 10^{10^(10^100)} + 999.

    • Table 2: Factors of 1000 números up to googolduplex: range 10^{10^(10^100)} − 999 to 10^{10^(10^100)}.

    • Table 3: Known factors of googolduplex minus 1, that is, 10^{10^(10^100)} − 1.

    • Table 4: Known factors of googolduplex minus 10, that is, 10^{10^(10^100)} − 10.

    • Table 5: Known factors of googolduplex plus 10, that is, 10^{10^(10^100)} + 10.

Cool math site of the week
August 30th, 2002.