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Review of Elementary Number Theory and Group Theory
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A2 A A2 algebraic integers algebraic number theory arbitrary Chapter XII characters class number class structure congruence conjugates consider contains COROLLARY cyclic group Dedekind define definition denote determined Dirichlet divides elementary equation equivalence classes Euclidean algorithm EXERCISE 13 EXERCISE 9 exists field discriminant finite number fundamental unit Gauss Hence ideal classes ideal factors ideal theory indecomposable integral coefficients integral domain Jacobi symbol lattice points Lemma linearly independent minimal basis modulo multiplication nonprincipal nonzero norm notation odd prime perfect square prime ideals principal ideal Proof prove quadratic field quadratic forms quadratic integers quadratic reciprocity R(Vd rational integers relatively prime representation residue classes residue classes modulo resolution modulus result satisfies Show solution solvable square-free symbol TABLE trivial unique factorization vectors verify whereas write zero