Number theory text that uses algebra?

Question

Could someone recomend a book on number theory that uses a lot of group theory and algebra to explain results? Like for example the proof that mod that is a prime power has a primitive root is simple if we observe $\mathbb Z_{p^\alpha}^{\times}\cong \mathbb Z_{(p-1)p^{\alpha-1}}$. Also noticin half of the elements $\bmod p$ are quadratic residues is immediate if we look at it as a cyclic group. Or as a final example fermat and euler are immediate consequences of lagrange.

I'm looking for a book that treats results from this perspective.

Thank you very much in advance.

Regards.

Answer 1

I highly suggest A Classical Introduction to Modern Number Theory, which uses algebra (and analysis upon occasion) whenever convenient.

Answer 2

Elementary Number Theory: An Algebraic Approach by Ethan Bolker immediately comes to mind. It's got a long list of errata, though.