Articles and calculators about Number Theory
- Number Theory articles and calculators
This site features:
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.
Quadratic modular equation solver: Calculator that can solve equations of the form ax2 + bx + c = 0 (mod n).
Sum of powers: Table of relations of the form ap + bq = cr with 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 BaseExponent = 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.
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.
Brilliant numbers: Interesting problem about products of primes of the same size.
Factors of Modified Fermat Numbers: Factors of numbers of the form 43n+23n+1 and 43n-23n+1.
Factors of numbers near googolplex (1010^100):
Table 1: Factors of 1000 numbers starting from googolplex: range 1010^100 to 1010^100 + 999.
Table 2: Factors of 1000 numbers up to googolplex: range 1010^100 − 999 to 1010^100.
Table 3: Factors of googleplex plus powers of 10, this is, numbers of the form 1010^100 + 10Exp, where 0 <= Exp <= 9.
Table 4: Known factors of googolplex minus 1, that is, 1010^100 − 1.
Table 5: Known factors of googolplex minus 10, that is, 1010^100 − 10.
Table 6: Known factors of googolplex plus 10, that is, 1010^100 + 10.
Factors of numbers near googolduplex (10googolplex):
Table 1: Factors of 1000 números starting from googolduplex: range 1010^(10^100) to 1010^(10^100) + 999.
Table 2: Factors of 1000 números up to googolduplex: range 1010^(10^100) − 999 to 1010^(10^100).
Table 3: Known factors of googolduplex minus 1, that is, 1010^(10^100) − 1.
Table 4: Known factors of googolduplex minus 10, that is, 1010^(10^100) − 10.
Table 5: Known factors of googolduplex plus 10, that is, 1010^(10^100) + 10.