Number Theory Integer Types

by Michael Carter

Carl Friedrich Gauss was known as one of the top ten greatest mathematicians. He was known as the prince of mathematics. Gauss is quoted calling mathematics the "queen of the sciences" and calling number theory the "queen of mathematics." Number theory is called "higher arithmetic." Number Theory is the study of whole numbers and sometimes spills over to rational numbers. The whole numbers that is the most fascinating are the primes. We know very little about the primes. Because we know so little about the primes we can make encryption for banks and computer security systems. We also have another fascinating number that we know more about, the composite numbers. The composite numbers are composed of two or more prime's products.

There are approximately 10 fields within Number Theory: Elementary, Analytic, Algebraic, Geometry, Combinatorial, Computational, Arithmetic Algebraic, Arithmetic Topology, Arithmetic Dynamics, and Modular Form. All these fields can take advantage of this maple package.

This Maple package is called inttypes, which is short for Integer Types. The inttypes package provides over 160 whole number types for Number Theorists to explore numbers. This package may be used as a tool for an academic course, Maple programming, or for research. It is also fun to play with these types for exploration and developing intuition about numbers. In addition, to these number theory integer types, this package also offers three very important functions: ithcomposite, ithprimorial, and printtypes. Maple have a function called, ithprime; which is used to find a particular prime based on its order. This inttypes package provides a function that gives a particular composite number based on its order, called ithcomposite. There is also an ithprimorialfunction that provides a particular primordial number based on its order. Finally, we have a function that will search among all the types of this package for a particular number and print its type. Srinivasa Ramanujan's taxicab number, 1729, is a good test for printtypes (see below). The number, 3, is also a good test for the printtypes function. On the Number Theory Types Test: Just change the integer on each of the for-loops for larger tests when testing the number theory types.

All types return a Boolean value of either true or false. It does not return a number. Note in the testing of the types below we can give input but the output is true or false. The input integer is not the output, hence, do not get confused and begin believing that the input is the output.

Finally, there is an official website for referencing and testing the integer types: "The On-Line Encyclopedia of Integer Sequences™ (OEIS™)" located at: http://oeis.org/

I hope you enjoy this package as much as I enjoyed creating it for you.

Cheers.