Please post your comments about the book under this post. If you have a review, we would be happy to hear about it here. If you find any errors, please state them here and we will give you credit in the next editions of the book.

**EDIT. **I’ve added LaTeX support to the website. Write your formulas between dollar signs to get them rendered by MathJax. -AHP

Testing the first LaTeX comment: $x^n + y^n = z^n$.

All the content is amazing.

I thought I know a lot about numbers theory and its beauty until I begun to read this book.

Very professional,with all branches of the Numbers Theorywell exposed,this book brings me to a superior level of knowledge.

I am grateful to Amir vor this unique opportunity.

I rate it 10/10.

I was fortunate enough to read the first chapter of Topics in Number Theory a few days ago. It’s been a long time since I haven’t dealt with number theory and I expected to not understand much of it but I was really surprised. The chapter begins with basic concepts explained in friendly language which really encourages you to keep on reading. Propositions are supported with proof and sufficient examples leaving you with no obscure points.

I also introduced this chapter to my sister who is a high-school student. While She had not heard about number theory and started this chapter with her high-school knowledge in mathematics, it really grasped her attention. This book is filled with solved problems and exercises which can be very helpful to students who intend to participate math contests. In conclusion, I believe that with simple and attractive language used by Amir and Masum, this book can be very useful for the people interested in mathematics and specially in number theory.

This book is a piece of true art, an eloquent text presenting to us one of the most beautiful topics in maths, Number Theory. Personally, I find results in this field simply fascinating, as beautiful results are born out of simple words. But the intricacies of this topic are far beyond others. This book though, makes many results accessible to a high school student and kindles the fire of passion and love for number theory in one.

The best part about this book is its simplicity. The authors tried to achieve something difficult from this book- to help the reader pace up with olympiad number theory starting from basics, and they have succeeded splendidly.

The book has 5 chapters overall. The first being divisibility, including all the prerequisites that are needed by a high school student who desires to start up with this wonderful subject.

The second one is Modular Arithmetic. This one is a bit special, as it does not only include the standard definitions, but also a bunch of useful theorems and tricks that, for some reason, are overlooked by most authors.

The third one is Arithmetic Functions. This is one of those hard topics, in my opinion, which has almost no theory, but the problems are quite hard. This chapter in this book, on the other hand, presents all the nuances of this topic. This is also an introduction to analytic number theory, which helps to make a really smooth transition from an olympiad number theory to advanced number theory!

Primes, the fourth chapter, is the topic which proposes the hardest of the challenges, even to number theorists. This book is an amazing way to start learning the properties of these mysterious numbers.

Finally comes my favorite, chapter 5. It contains topics from the true perspective of a problem solver, with various tricks of the trade, and also some topics that are not generally given in other books, such as Thue’s lemma, Lifting the Exponent, the Darij-WolstenholmeTheorem etc. This chapter teaches a student how to ‘think like a mathematician’.

In a nutshell, this is one of those gems which deserves a place in every maths enthusiasts’ shelf. This book presents the correct mixture of theory and loads of problems, which can help anyone to learn the ‘science of numbers’!

I was fortunate enough to sweep through this Book over and over in order to scrounge any problems it may have. And I must say that it manages to contain no errors at all, and at the same time, offers comprehensive and well conceived content.

Formatting is another factor that makes this book a desirable purchase for anyone interested in thriving in Math and Numbers Theory in particular. It has one of the most professional and easily accessible formatting systems available in the mass market; even compared to more famous and reference books. This feature makes the content more easily understood and accessed by the reader by removing the barrier of formatting and its complexity.

And finally, thanks to the authentic questions and content available among the pages of this book, it’s an easy recommendation for anyone looking to strengthen their Numbers Theory mentality and/or participate in various Olympiads.

Amazing job. I had the chance to look at this book page by page in order to find some issues and mistakes, but boy it was one tough thing to do. Everything is in order and precise. It’s totally a fruitful book in number theory, and the short name of it indeed fits, for it is a bomb of knowledge. A special bravo to writers because of this legit work.

Who want to get gold on IMO, then must learn something from this book.

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