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What is the best book for a beginner in Introduction to number theory?

I am new to this field and getting deeper into cryptography, so I think reading some intro books about number theory can be of help.

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    $\begingroup$ A reference request like yours is too broad for Stack Exchange -- you ask for a survey of a whole research area! You need to narrow your focus considerably before a question of reasonable scope appears, and you also need to include criteria that allow to say that and why one answer is better than another (why is not "any book on the topic" an answer?). Try talking to your advisor(s), search with Google Scholar and check out this guide to better (re)searches on Academia. $\endgroup$ – Raphael Feb 9 '15 at 18:12
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    $\begingroup$ Dear Raphael, the question I believe is more than clear and direct and is not too broad. This forum is called 'Stack Exchange', which is what what precisely my questions begs. An exchange of ideas. No one, as far as I can see (hear, sense and smell) has asked for a survey of a whole research area. Putting the question on hold is a big sign of disrespect and arrogance. $\endgroup$ – tony9099 Feb 9 '15 at 18:25
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    $\begingroup$ Your individual opinion notwithstanding we have certain community standards, and your question fails to meet them. As a moderator my task is to uphold said standards, so going all ad hominem in my direction is futile. If you take issue with my decision, feel free to flag for reopening (hint: you may want to heed my above comment first) or raise the issue on Computer Science Meta. $\endgroup$ – Raphael Feb 9 '15 at 18:29
  • $\begingroup$ tony9099, Raphael is exactly right. Our moderators merely enforce standards and policies established by the community. I realize that if you're new to the site you might not be familiar with some of these policies. If you have questions about site policies, you're welcome to visit Computer Science Meta to learn more. But please treat our moderators with respect. They have a thankless job, but they are vital to the success of the site. They volunteer their time and I for one am very grateful for their work. Rest assured that they're not on a power trip; they're merely enforcing policies set by the community. $\endgroup$ – D.W. Feb 9 '15 at 23:01
  • $\begingroup$ Dear D.W nobody is disrespecting anyone. How dare you insult me such cheap accusations. I can not find any word of disrespect in my comment. If you do, that is your problem. $\endgroup$ – tony9099 Feb 10 '15 at 13:38
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If you want to go deeper into cryptography and number theory, then of course you start here: Neal Koblitz, A Course in Number Theory and Cryptography.

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  • $\begingroup$ Thanks. I am reading now Applied Cryptography by Bruce Schneier. It is okay, but does not get deep inside the maths a lot. $\endgroup$ – tony9099 Feb 9 '15 at 16:29
  • $\begingroup$ Well, that's probably why it's called Applied Cryptography. Koblitz starts with two chapters of pure number theory, and then goes on to build cryptography upon it. So if you want to understand the math part, use that book. There are certainly other books with more number theory to go into once you're done with that. $\endgroup$ – john_leo Feb 9 '15 at 16:37
  • $\begingroup$ Okay John. I will do as you suggest. I think its a good way to start building up some notions about crypto. $\endgroup$ – tony9099 Feb 9 '15 at 16:41
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    $\begingroup$ And why do you recommend this book over (all) others? $\endgroup$ – Raphael Feb 9 '15 at 18:14
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    $\begingroup$ This is how we have been dealing with unspecific book requests (cf here and here). If you think it's the wrong policy, you are invited to post on Computer Science Meta, too. $\endgroup$ – Raphael Feb 9 '15 at 19:39

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