The study of natural numbers, for their own sake, is an ancient diversion. Problems such as finding integer solutions for the familiar Pythagorean equation x² + y² = z² were solved as early as 1600 B.C. by the Babylonians. Pierre Fermat (early 1600's A.D.) claimed that no integer solutions exist for xⁿ + yⁿ = zⁿ for n greater than 2. This claim baffled mathematicians for almost 400 years, as they searched for either a proof or a counterexample. Finally in the 1990's, an English mathematician, Andrew Wiles, devised a very complicated proof for this simple statement.

This is but one example of the many problems in number theory that can be simply stated and easily understood. Much of modern mathematics is inaccessible to the uninitiated. Mountains of technical knowledge are required to understand even the statement of the problems. Happily, number theory does not present these difficulties.

8.1 The building block of addition

8.2 How can I build thee? Let me count the ways

8.3 Building blocks for subtraction

8.4 The Euclidean algorithm

8.5 The building blocks of multiplication