Abstract
The importance of the notion of prime number should be evident from the results of Chapter 1.
In this chapter we shall give several proofs of the fact that there are infinitely many primes in ℤ. We shall also consider the analogous question for the ring k[x].
The theorem of unique prime decomposition is sometimes referred to as the fundamental theorem of arithmetic. We shall begin to demonstrate its usefulness by using it to investigate the properties of some natural number-theoretic functions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer Science+Business Media New York
About this chapter
Cite this chapter
Ireland, K., Rosen, M. (1990). Applications of Unique Factorization. In: A Classical Introduction to Modern Number Theory. Graduate Texts in Mathematics, vol 84. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2103-4_2
Download citation
DOI: https://doi.org/10.1007/978-1-4757-2103-4_2
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3094-1
Online ISBN: 978-1-4757-2103-4
eBook Packages: Springer Book Archive