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Lemma Uniqueness of Prime Factorization
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Abelian group arithmetic progression chapter characters modulo coefficients common divisor common fractions congruence classes contains convergence coprime COROLLARY cyclotomic equation decimal expansion deﬁned deﬁnition denominator Dirichlet divides element equal Euclid’s lemma Euler exists exponent Farey sequence ﬁnd ﬁnite ﬁrst following theorem Ford circles formula fulﬁlled Gauss Gaussian sums hence implies inequality inﬁnite number integers Jacobi symbol kth root Lagrange resolvents lattice points Legendre symbol log L(s mod ml modulo 17 multiple number of lattice number of primes number theory obtain odd numbers odd primes period polynomial positive integer prime factors prime number primitive congruence root primitive root modulo primitive solution problem proof proper reduced fraction proved quadratic nonresidues quadratic residue rational number residue classes residue classes modulo root of unity satisﬁes sequence of order shows sieve square summand twin primes uniqueness of prime unity of order Viggo Brun write