chapter  5
3 Pages

Fermat, Euler, and Gauss

The Elements are divided into 13 books. Three of these deal with number theory; the other books are concerned with plane and solid geometry, and the construction and properties of real numbers. The discussion of number theoretic problems begins in Book VII. In it we find the definitions of prime and com­ posite numbers, and the method for computing the greatest common divisor by successive divisions. Book VIII is mainly concerned with geometric progres­ sions. Book IX contains the proof that there are infinitely many primes, which we discuss in Chapter 3, section 5; and a formula for perfect numbers, which can be found in the exercises of Chapter 2.