multiplicative number theory
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§27.3 Multiplicative Properties… ►
§27.8 Dirichlet Characters… ►An example is the principal character (mod ): … ►If , then the characters satisfy the orthogonality relation … ►A divisor of is called an induced modulus for if … ►If is odd, then the real characters (mod ) are the principal character and the quadratic characters described in the next section.
Mathematica. PrimeQ combines strong pseudoprime tests for the bases 2 and 3 and a Lucas pseudoprime test. No known composite numbers pass these three tests, and Bleichenbacher (1996) has shown that this combination of tests proves primality for integers below . Provable PrimeQ uses the Atkin–Goldwasser–Kilian–Morain Elliptic Curve Method to prove primality. FactorInteger tries Brent–Pollard rho, Pollard , and then cfrac after trial division. See §27.19. ecm is available also, and the Multiple Polynomial Quadratic sieve is expected in a future release.
For additional Mathematica routines for factorization and primality testing, including several different pseudoprime tests, see Bressoud and Wagon (2000).
Number Theory Web. References and links to software for factorization and primality testing.