Some basic number theory algorithms, allowing you to find the sum, difference and product (mod n), represent integers as the sum of two squares or as the sum of a square plus a multiple of another square, find the gcd, directly or step by step, of two numbers, determine if two numbers are relatively prime, use Euler Phi function to determine the number of relatively prime numbers there are to an integer, find multiplicative inverses (mod p), solve linear equation (mod n), solve a system of equations with multiple moduli and remainders (Chinese Remainder Theorem), use the Fast Powering algorithm f exponentiation (mod n), find primitive roots (mod p), find quadratic residues of an integer, determine if an integer has a square root (mod p), if so, find the square root (mod p), use the Jacobi Symbol, apply the Gauss Criterion, solve any quadratic equation (mod p), find idempotents of Z/nZ, find invariants of indempotents in Z/nZ, use the Solovay-Strassen, the Miller-Rabin test or the "wheel" for testing primality, factor an integer into product of primes, find the next prime starting at any integer, find the next prime with remainder r, modulo n. The HP 49 version has additional programs added to generate Pythagorean triangles, generate the Egyptian fraction decomposition of any fraction, and find the smallest solution to the Pell equation x*x - N*y*y=1, for fixed N>1. |