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These notes are intended for a graduate course in Number Theory. No prior familiarity with number theory is assumed.

Chapters 1-14 represent almost 3 trimesters of the course. Eventually we intend to publish a full year (3 trimesters) course on number theory. The current content represents courses the author taught in the academic years 2020-2021 and 2021-2022.

It is a work in progress. If you have questions or comments, please contact Peter Veerman (

Publication Date



Number theory -- Study and teaching (Higher), Arithmetic -- Foundations, Diophantine equations, Prime numbers, Continued fractions, Additive functions, Modular arithmetic


© 2022 J. J. P. Veerman

Creative Commons License
This open access textbook is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.


Part 2. Topics in Number Theory is available online at underneath the MTH 410/510, Number Theory heading (see lecture notes)

March 2022, corrections and slight additions to chapters 1-11 and chapters 12-14 were added.

June 2021, corrections and slight additions to chapters 1-6 and chapter 7-11 were added.

Persistent Identifier

An Introduction to Number Theory

Included in

Number Theory Commons