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Elementary number theory learning recommendations

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This page provides subject-specific learning recommendations for the subject elementary number theory. See all our learning recommendations pages |
NOT TO BE CONFUSED WITH arithmetic in the sense of computation and number sense. For recommendations on arithmetic, see arithmetic learning recommendations

Elementary number theory is a fascinating discipline of mathematics that modestly extends the base of arithmetic knowledge acquired in elementary and middle school and in the process lays the foundation for ideas of abstract algebra. It can also serve as an excellent introduction to the general mathematical way of thinking, including mathematical exploration, hypothesis formulation, and proof discovery. It is also a topic neglected from many undergraduate mathematics curricula, and is typically offered as an optional course rather than a component of the standard mathematical course sequences.

Elementary number theory is also an important component of contest mathematics.

Top recommendations

Best books

Book Author ISBN and purchase links Price estimate (approximate value, international editions may be cheaper) Why we're recommending it
Elementary Number Theory (Springer Undergraduate Mathematics Series) [Paperback] Gareth A. Jones and Josephine M. Jones (popularly known as Jones & Jones) ISBN 978-3540761976, Amazon paperback $25-50 covers all the standard topics of elementary number theory well
Elementary Number Theory: Second Edition (Dover Books on Mathematics) [Paperback] Underwood Dudley ISBN 978-0486469317, Amazon paperback ~$9 (Kindle, paperback), ~$120 (hardcover) We recommend it mainly on account of price, and on account of the fact that the range of topics is sufficiently straightforward that quality variation is not huge.

Free online books

These are available free, making it useful to have them as supplements, even though they may not be suitable as primary texts: