Hi, I'm an undergraduate math student. I've already passed linear and abstract algebra and recently passed a course in elementary number theory and I really enjoyed it.
now I wanna self-study more books this semester and I'm searching for good books with exercises.
my most interest is in solving diophantine equations and their applications.
tnx for your suggestions btw and sry for my bad English :)
There is a large bibliography on Number Theory, but many of these books are very expensive; For this reason, below I give you a link where you can find a lot of material to download freely:
https://www.topfreebooks.org/free-textbooks-in-mathematics-number-theory/
www.topfreebooks.org is a links sharing website. We only share the download links of public domain books or the books that we believe are out of copyrights available. We never host, scan or upload any book or literary content on our servers or anywhere else.
Dear Arsalan Hasanvand ,
You can do some google search and create your personal collection of readable articles and papers based on your academic level.
For example,
http://www.msri.org/~levy/files/Book44/01lenstra.pdf
is a readable paper by a new graduate student.
Best regards
Dear Arsalan Hasanvand
Besides Lang's, you can read L.E. Dickson's, H.Cohen's. Dickson: History of Number Theory should be really helpful to you if just beginning. Airthmetca by Diophantus if you can lay your hands although I have not read
Best Wishes
Saroj
I tried using Elementary Number Theory by Jones and Jones for exactly the same purpose as stated in your question. However, I found that with my limited mathematical background (even though I’ve written and had published a paper) I wasn’t able to teach this material to myself; I really need someone to teach it to me which I hope to do some day. Perhaps with your background you won’t have this difficulty. The book itself I think is probably quite good.
Google search my paper “On the solution of the cubic Pythagorean Diophantine equation x^3+y^3+z^3=a^3” and let me know whether it’s of any interest to you. It was published in 2006 in the Missouri Journal of Mathematical Science.
Louis John Scheinman, it was really good! yeah, actually I'm interested in that field.
In order to give a good answer, I think, it would be necessary to know what is your background...
Antonio M. Oller-Marcén I'm a bachelor's student. I've passed elementary number theory, abstract algebra, and linear algebra. I don't know what else to say. :)
It is important to know, because that background leaves out analytic number theory for which some knowledge of complex vraiable functions could be required...
Antonio M. Oller-Marcén unfortunately, I haven't studied complex functions or analysis yet.
I study numerical semigroups rather than diophantine equations. I am using this book
https://link.springer.com/book/10.1007/978-1-4419-0160-6
Meral Süer I hadn't heard of them! it seems to be interesting! thank u!
you can use this book,
An Introduction to Diophantine Equations: A Problem-Based Approach
Book by Dorin Andrica, Ion Cucurezeanu, and Titu Andreescu
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