1
$\begingroup$

I'm an undergraduate student and I would like to learn olympiad level-number theory. For what I've read, Number theory: Structures, Examples and Problems is a great book, however, I'm not sure it is a good book to learn the subject. I've skimmed through the first pages and it seems that some of the problems require one to have a little knowledge of number theory, but I'm not completely sure about it. I would like a book that gives you strong background and also I would like that the book doesn't need any abstract algebra knowledge to be read (I have almost zero knowledge of abstract algebra) and if possible, a book that offers hard problems (like those encountered in olympiads).

Also, I would like to add that, at least right now, I'd like to learn number theory to participate in an olympiad.

I'd also like to add that I didn't consider 104 Number Theory Problems: From the Training of the USA IMO Team because I read somewhere (I think it was in the AoPS site) that it is more a "problem book".

Thank you for your help!

$\endgroup$
3
  • $\begingroup$ I can't suggest much, but learning some basic abstract algebra is certainly a good way to go. Try to learn modular arithmetic, as it is, for instance, a basic tool to tell if an equation has no solutions in $\mathbb{Z}$. Abstract algebra is here to help. $\endgroup$
    – Shoutre
    Commented Aug 17, 2016 at 1:03
  • $\begingroup$ I know, I plan to start stufying abstract algebra next semester (right now I'm just TOO BUSY to do so) $\endgroup$
    – Hugo VH
    Commented Aug 17, 2016 at 1:15
  • $\begingroup$ You can tell that $x^{2}=2$ has no solutions in $\mathbb{Z}$ because such a solution $x$ would have to be multiple of $2$ and its square would be a multiple of $4$, yielding a contradiction. Modular arithmetic extends this idea by looking at divisibility by some other integers to 'detect impossibilities' and it is very useful in this kind of problem. You don't need abstract algebra to learn this and most elementary books cover it. I'm not so sure what level are you talking about, so I hope this helps. $\endgroup$
    – Shoutre
    Commented Aug 17, 2016 at 1:25

1 Answer 1

Reset to default
1
$\begingroup$

To be honest, I am not sure what "olympiad level" is.

For learning at the elementary level, you might start with this: https://www.amazon.com/Three-Pearls-Number-Theory-Mathematics/dp/0486400263

Then try this: https://www.amazon.com/Number-Theory-Pure-Applied-Mathematics/dp/0121178501#reader_0121178501

This book seems geared specifically for olympiads: https://www.amazon.com/104-Number-Theory-Problems-Training/dp/0817645276/ref=sr_1_2?s=books&ie=UTF8&qid=1471395975&sr=1-2&keywords=olympiad+mathematics+number+theory

$\endgroup$
1
  • $\begingroup$ Thank you, I'll check those books $\endgroup$
    – Hugo VH
    Commented Aug 17, 2016 at 1:18

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .