Preface
This is a first draft of a free (as in s peech, not as in beer, [Sta02]) (although it is free as in
beer as well) undergraduate number theory textbook. It was used for Math 319 at Colorado
State University –Pueblo in the s pring semester of 2014 . Thanks are hereby offered to the
students in that class – Megan Bis sell, Tennille Candelaria, Ariana Carlyle, Michael De-
graw, Daniel Fisher, Aaron Griffin, Lindsay Harder, Graham Harper, Helen Huang, Daniel
Nichols, and Arika Waldrep – who offered many useful suggestions and found numerous
typos. I am also grateful to the students in my Math 242 Introduction to Mathematical Pro-
gramming class in that same s pring semester of 2014 – Stephen Ciruli, Jamen Cox, Graham
Harper, Joel Kienitz, M atthew Klamm, Christopher Martin, Corey Sullinger, James Todd,
and Shelby Whalen – whose various programm ing projects p roduced cod e that I adapted
to make some of the figures and examples in the text.
The auth or gratefully acknowledges the work An Introductory Course in Elementary
Number Theory by Wissam Raji [see www.saylor.org/books/] from which this
was initially adapted. Raji’s text was released under the Creative Commons CC BY 3.0
license, see creativecommons.org/licenses/by/3.0 .
This work is i n stead released under a CC BY-SA 4.0 license, see
creativecommons.org/licenses/by-sa/4.0 . (The
difference is that if you build fu ture works off of this one, you must also release your
derivative works with a license that all ows further remi xes over which you have no control.)
This version: 07 May 2014 11:04MDT. Note this text will be frequently updated and
improved as the author has time, particularly during and immediately after semesters in
which it is b eing used in a class. Therefore please check back often to t he website, which
is www.poritz.net/jonathan/share/yaintt.
This work i s dedicated to my insanely hardworking colleagues at Colorado State Uni-
versity – Pueblo whose dedication to their students, their schol arship, and their comm uni-
ties is an inspiration. While I was working on the first version of this boo k, those colleagues
stood u p to some of the most benighted, ignorant admini strative nonsense I have seen in
the more than thirty years I have been involved in h igher education. As MLK said, “The
arc of the moral universe is long , but it bends towards justice.” – It is selfless, i ntelligent,
hard work like yours that is doing the bending.
Jonathan A. Poritz, 7 May 2014, Pueblo, CO, USA
iii
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