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Number Theory (Dover Books on Mathematics)

George E. Andrews · 2 HN comments
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Amazon Summary
Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic. In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems. Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory. Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated..
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At that age, I enjoyed Number Theory by George E. Andrews

https://www.amazon.com/Number-Theory-Dover-Books-Mathematics...

There is an elementary number theory textbook by the famed number theorist and Ramanujan scholar Dr. George Andrews called Number Thoery, http://www.amazon.com/Number-Theory-Dover-Books-Mathematics/...

It contains proofs of very many results from elementary number theory, like Fermat's Little Theorem here. The reason this book is different from any other is because the proofs are all combinatorial, like counting beaded necklaces or otherwise. It is also a Dover book, meaning it costs very little. It is also one of the books I used as reference to create the elementary number theory course that I sometimes teach.

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