Need a Good Introduction to Number Theory? Check Out These Proven Resources!

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  • Thread starter moriheru
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In summary, there were several book recommendations for an Introduction to Number Theory with exercises and proofs. Two highly recommended books were "Hardy and Wright" and "Apostol - Introduction to Analytic Number Theory". Additionally, there were suggestions for resources on mathematical proof techniques, such as "How To Prove It" by Daniel J. Velleman and "Elementary Number Theory" by Rosen, which includes solutions to problems.
  • #1
moriheru
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Can anyone recommend a good Introduction to Numbertheory with excercises and of course proofs

Thanks for any recomendations.
 
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  • #3
Nevermind...Hardy and Wright is brilliant.
 
  • #4
George E. Andrews - Number Theory
Apostol - Introduction to Analytic Number Theory

These two books are great, I had not the time to finish to read them entirely yet. You'll find lot's of proof in them. I don't know if there is a solution manual for either of them but in Andrew's book you'll find a section "hint and answer" and there is a nice bibliography at the end of both books.

If you want to know more about mathematical proof in general you'll find a free good book on the website of the author: http://web.maths.unsw.edu.au/~jim/proofs.html (you have to scroll down a little bit to find the links to the pdf's...)
An other one is : Daniel J. Velleman - How To Prove It, published by Cambridge University Press.

Often they use theorems in Number theory as example in "Proof Theory". They show the different ways of proving things and depending of the problem you'll know what type of proof is adequate, how to make a strategy, etc...
 
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  • #5
If you want problems with solutions, you may want to check out Rosen's Elementary Number Theory since there are solutions to the problems.
 
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  • #6
Thanks all, very helpfull.
 

Related to Need a Good Introduction to Number Theory? Check Out These Proven Resources!

1. What is number theory?

Number theory is a branch of mathematics that focuses on the properties and relationships of numbers, particularly integers. It is one of the oldest and most fundamental areas of mathematics and has applications in many other fields such as cryptography, computer science, and physics.

2. What are the basic concepts in number theory?

The basic concepts in number theory include prime numbers, divisibility, modular arithmetic, and congruences. These concepts are used to study the properties of numbers and their relationships with each other.

3. What is the importance of number theory?

Number theory is important because it helps us understand the fundamental properties of numbers and their behavior. It has practical applications in cryptography, coding theory, and computer science, and has also been used in solving real-world problems such as the distribution of prime numbers.

4. What are some famous problems in number theory?

Some famous problems in number theory include the Goldbach Conjecture, the Riemann Hypothesis, and Fermat's Last Theorem. These problems have fascinated mathematicians for centuries and have led to significant advancements in the field of number theory.

5. How is number theory used in cryptography?

Number theory plays a crucial role in cryptography, which is the study of secure communication. It is used to develop algorithms and protocols for secure encryption and decryption of data. For example, the RSA algorithm, which is widely used in secure communication, is based on number theory concepts such as prime factorization and modular arithmetic.

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