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Acknowledgements Acknowledgements

This text evolved over the course of teaching MAT 338 Number Theory for many years at Gordon College, and immense thanks are due to the students through five offerings of this course for bearing with using a text-in-progress. The Sage Math team 3  and especially the Sage cell server 4  have made an interactive book of this nature possible online, and the PreTeXt 5  (formerly known as Mathbook XML) and MathJax 6  projects have contributed immensely to its final form, as should be clear. I’m particularly grateful to Rob Beezer’s answering questions and upgrading PreTeXt capabilities early and often.
In addition, I’d like to thank the many people who found errors or improvements since the January 2017 edition. Gordon College MAT 338 students Kevin Neil, Holly Gershman, Jess Wild, Julianne McKay, Ethan Kang, Joshua Yang, Hyunjun Park, Samuel Paquette, King Hunter, Richard Ryzi, Micah Martin, Dean Tengdin, and Abraham Holleran all contributed, as did Linfield University’s Brandon Perez. Internet users Pieter Geerkens, Jiekai Zheng, and niwox contributed useful fixes. Colleagues including Bucknell’s Sally Koutsoliotas, Longwood’s Phillip Poplin, USF’s Bruce Cohen, KU’s Marge Bayer, Biola’s Joseph DiMuro, Marian’s Matt DeLong, Maryland’s Todd Rowland, Western New England’s Caleb Shor, Boise State’s Zach Teitler, Nebraska-Omaha’s Keith Gallagher, The College of New Jersey’s Tom Hagedorn, and especially Puget Sound’s Mike Spivey all found key typos, tacit hypotheses, or broken links for me to fix and improve. Most importantly, George Jennings (emeritus of Cal State Dominguez Hills) spent many hours making hundreds of detailed suggestions (especially for clarifying proofs, exercises, and exposition); I gratefully thank him for his assistance, using ‘new eyes’ to look at text I’ve pored over too many times.
Finally, no acknowledgement would be complete without recognizing the patience of my family with respect to the days and weeks of travel, from an hour away in New England to as far away as Cape Town and India, in order to learn more about Sage and teach using Sage in the classroom. It was always done with the goal in view of enriching others’ lives and not just my own, and I hope I have lived up to that promise.