Till today, I was learning "Algebra", more than other subjects (analysis/topology). I thought, learning number theory may not be difficult for me.
Many theorems/statements in number theory are easy to state, but difficult to prove, in the sense, the tools required in the proof may be from real or complex analysis.
Looking some simple statements in Number Theory, I tried to give algebraic proof, but unsuccessful. Later I came to know that proving them requires "analysis". (Dirichlet's theorem on distribution of primes, or related theorems, for example.)
If the proof of some statement is based on "algebra", I can give my effort to write the proof. However, I couldn't handle easily, right now, the tools of analysis for the problems in number theory.
Can one suggest very elementary book on analytic number theory, in which, the use of tools of analysis is illustrated with examples?
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