Can anyone please recommend me a good number theory book to read? I want lots of answers to get a good idea. I am a 1st year university student, so it would be good if there are no deep terms and the theory is explained well.
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In my undergrad, we used Elementary Number Theory by Kenneth Rosen for our upper level (junior/senior) number theory course. There is also a solutions manual out there, which may be useful if you are self studying the book. To get the most out of the book, you should probably be familiar with the structure of mathematical proofs. For this I recommend the excellent (and free) Mathematical Reasoning Writing and Proof by Ted Stundstrom available here.
If you want something more basic, Discrete Mathemtics, also by Kenneth Rosen (particularly the first 4 chapters) would also be a good read. It covers proof writing (i.e. creating formal mathematical arguments), elementary mathematical structures (sets, functions), as well as some basic number theory such as:
- Divisibility and Modular Arithmetic
- Integer Representations and Algorithms
- Primes and Greatest Common Divisors
- Solving Congruences
- Applications of Congruences
- Cryptography
Evan Rosica
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