Dover Number Theory

Really a great book, consider theory plus many problems, but if you are just starting then don't go and try to solve everything from this book, as Many as you can solve,cuz more you do the more you will get familiar with the patterns and then you will be able to solve the problem you left. And I will also sujest that see some vedios of number theory in YouTube before buying, then you will not feel disheartened or unconfident. Happy solving.

good book

いわゆる平方剰余までの初等整数論の解説書であるが、数学専攻の学生を視野においた組み合わせ数学も随所に取り入れている。記述はふんだんに実例を取り上げて丁寧であるが定理等は簡潔にまとめられている。日本では、高木貞治の初等整数論が名著とされてはいるが、これは数学専攻の学生を対象としたかなり難解な書で、初学者にはハードルは高い。その点Number theoryは初学者には取っ付きやすく、高校の数学Aで学んだ学生にはスムーズに接続されるであろう。整数論は理科系の学生には基礎科目としては、通常カリキュラムには入っていない。しかし昨今ネットの暗号化、仮想通貨のブロックチェーンなどの時代の要請を鑑みると、整数論を学ぶことは理科系学生には必須と考えられる。その点で、このNumber theoryは英語も平易であるから整数論を学ぶ教科書として、十分選択肢になりうる。

A classic book that covers elementary number theory and some advanced topics as well. The author used a "discovery" approach that it's not common in most modern texts on Number Theory. Each chapter and section is about a "question" that the author explores, and then uses to establish the theorems and proofs. The exercises aren't too difficult, but they are good enough to keep you engaged. As a downside, I should say that the approach is not as easy to revisit as other books that go directly into "theorem/proof" without too much exposure.

I recently took a one-semester course using this text. I found it to be one of the best textbooks I've used so far. The exposition was clear and easy to digest, with just the right number of clarifications and examples. The exercises were numerous, challenging and illuminating. No background beyond very basic set theory is assumed, and in fact the writer goes very far out of his way to keep his exposition separate from abstract algebra. This is most evident in the chapter on primitive roots. I can't speak for the second half of the book, on additivity, but I can say with certainty that the first nine chapters are worth the effort.