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chapter oneUNIQUE FACTORIZATION
chapter twoAPPLICATIONS OF UNIQUE FACTORIZATION
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a e F algebraic integer algebraic number Chapter character of order characters of F coefficients complex numbers congruence conjecture consider Corollary cubic reciprocity cyclic D/nD defined definition divides equation Euclidean domain Exercise field with q finite field formula Gauss sums greatest common divisor hypersurface implies infinitely many primes irreducible polynomials Jacobi sums law of quadratic Legendre symbol Lemma Let F monic irreducible polynomials monic polynomial nonresidue nontrivial nonzero notice number of elements number of points number of solutions number theory odd prime ordp points at infinity polynomial of degree positive integer prime numbers primitive root mod primitive root modulo PROOF Let Proposition 4.2.1 prove q elements quadratic nonresidue quadratic reciprocity quadratic residue mod rational prime relatively prime result follows Riemann hypothesis root of unity Section Show Suppose Theorem unique factorization Z[co Z/mZ Z/pZ zero zeta function