Program:	NUMBER (also includes SUBCHIN and SUBFACT)
Author:		Rob Gaebler
Date:		1/15/02

NUMBER is a composite program with five operations to choose from.  When you
run NUMBER, you are given the following options:

1: Factor N, etc.
Factors N, Finds the number, sum, and product of the divisors, and computes
phi(N), the number of numbers less than N that are relatively prime to N.

2: Chinese Remainder Theorem
Finds the unique solution to a set of congruences.  For example, if you want to
find what number is 5 mod 7, 6 mod 37, and 0 mod 4, you would input the residue
list {5, 6, 0} and the mod list {7, 37, 4}.  The answer is given as 376 mod
1036, since any number that is 376 mod 1036 satisfies the given congruences.
The Chinese Remainder Theorem, by the way, guarantees that there is only one
solution.  Not every set of congruences has a solution, of course.  In such
cases the program outputs "No Solution."

3: AX+BY=C
Solves the linear Diophantine equation Ax+By=C.  You input the constants A, B,
and C, and the program finds solutions for X and Y.  If there is no solution,
the program tells you so.

4: Mod
Computes N mod M.  N and M can both be either an integer or a list of
integers.  Thus there are 4 possible types of input: number mod number, number
mod list, list mod number, or list mod list.  Example: If N = {5,47,36,11} and
M=7, the answer is {5, 5, 1, 4}.  If both N and M are lists, they must have the
same length.

5: Prime List
Finds all the primes between the two bounds that you input.

Feel free to contact me with questions or comments at rgaebler@hmc.edu.
