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

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For those seeking an introduction to number theory with exercises and proofs, several recommendations emerged in the discussion. Hardy and Wright's book is highlighted as an excellent resource, along with George E. Andrews' "Number Theory" and Apostol's "Introduction to Analytic Number Theory." Both Andrews and Apostol provide numerous proofs and include helpful sections like "hints and answers," though it's unclear if solution manuals are available. For a focus on mathematical proof techniques, "How To Prove It" by Daniel J. Velleman is suggested, as it incorporates number theory examples to illustrate various proof strategies. Additionally, Rosen's "Elementary Number Theory" is noted for including solutions to problems, making it a practical choice for learners. A free resource on mathematical proofs is also available on the author's website, offering further support for those interested in the subject.
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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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Nevermind...Hardy and Wright is brilliant.
 
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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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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Thanks all, very helpfull.
 

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