Abstract
This chapter discusses continued fractions and indeterminate equations. Any positive rational number can be represented in the form of a so-called continued fraction. The process of finding the greatest common divisor of two numbers by means of consecutive divisions is called Euclid's algorithm. The properties of terminating fractions hold infinite continued fractions and permit the finding of rational numbers as close as desired to sufficient partial denominators. An indeterminate equation is an equation for which there is more than one solution. For example, 2x = y is a simple indeterminate equation, as are ax + by = c and x2 = 1. Indeterminate equations cannot be solved uniquely.
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