ABSTRACT
This chapter presents the fascinating structure that emerges from attempting to divide in a commutation ring Z. The quickest way to find out whether one integer is a multiple of another, if they are not too big, is to divide one by the other on a calculator. Any integer whatsoever is either a multiple of 10, or else sits between two uniquely determined multiples of 10. As the norm of a Gaussian integer is a nonnegative integer, it is tempting to wonder whether every nonnegative integer is the norm of some Gaussian integer. The degree of a polynomial is the exponent of the highest power of X that occurs in it; the leading coefficient is the coefficient of that highest power of X. A polynomial is monic if its leading coefficient is 1.
