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I know the basics of logic, sets, relations and the like, so studying intros to abstract algebra and real analysis is not that hard. That said, I have a deficiency when it comes to elementary number theory and combinatorics topics. Things like divisibility, modular arithmetic, congruences, prime numbers and such like regularly pop up as examples to illustrate certain topics in analysis.

What are some very concise books or, maybe, online resources for learning these topics from number theory and combinatorics? Since I need to know them to understand what's going on in other subjects I probably need the bare minimum.

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For an elementary book in combinatorics I recommend Combinatorics Through Guided Discovery, available for free here

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Ore's Invitation to Number Theory is free, short, elementary and has all the topics you listed, an even shorter option is the number theory wikibook. These online lecture notes have short chapters on counting and combinatorial probability, and this webpage has all the combinatorial topics that you'll likely need.

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  • $\begingroup$ Is the link to Ore's book a copyright violation? $\endgroup$ – lhf Jun 18 '14 at 11:33
  • $\begingroup$ I don't know, it comes up third in the google search on "Invitation to Number Theory Ore". $\endgroup$ – Conifold Jun 18 '14 at 18:38
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Check out "Introductory Combinatorics $5$th edition" by Richard A. Brualdi and "Elementary Number Theory $7$th edition" by David Burton. You can find these books online.

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