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I know it is a very general question, but i'm not sure how to get started and improve number theory related skills related to ACM ICPC and other programming competitions.Any good way or book recommendations ?

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Finding problem sets to practice on, and doing a lot of practice would be a part of what you're supposed to do. – J. M. Oct 27 '10 at 15:06
A good book in my opinion is 104 Number Theory Problems From The Training Of The USA IMO Team, by T. Andreescu, D. Andriga and Z. Feng… – Américo Tavares Oct 27 '10 at 15:17
thanks guys for suggestions "104 problems in Number theory by T.Andreescu" seems good to brush up topics before ACM. – user2860 Oct 31 '10 at 18:58

Well, i am not anyone great in answering this question, but atleast on my behalf, i shall tell you some good introductory books:

  • Introduction to theory of numbers by David Burton

  • Introduction to theory of numbers by G.H.Hardy, E.M.Wright

  • Introduction to Analytic number theory by Tom Apostol

  • 104 problems in Number theory by T.Andreescu

All the above books are getting a very good foundation on the subject. As i said, i am no one to answer, this as i myself struggle in solving problems. But Solving problems are the only way one learns a subject. There are many peers, who would like to answer this question, and you can learn a lot from them!

Happy Reading!

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For the ACM you should probably focus on their problem sets and could also look into problems from discrete mathematics. I really don't think they ask questions that rely on a graduate level understanding of number theory so reading books could be overkill for your purposes and would only confuse you if you rush it. It should take several weeks to read several chapters in a good number theory book - assuming you're not too busy (but you're in cs, right?).

Short answer: Go and ask a math professor for some problem sets.

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