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1.4 implies absolute value absolutely continuous absolutely irreducible Acta Arith additive arithmetic function algebraic number field arbitrary arithmetic function assume branch cycles coefficients component conjecture conjugates contains contradiction Corollary defined definition denote Diophantine diophantine approximation distribution divisor Ecjih effectively bounded effectively computable elements equation estimate exists F)n having order fc-tuples finite field follows Gaussian integer GF(g GF(q Hence inequality interval irreducible polynomials irreducibles of degree JieMMy Let F limsup Math matrix fields Mersenne prime minimal polynomial multiples nombres non-negative integers non-zero norm-perfect number number of distinct Number Theory obtain occur odd integers one-one order pm perfect numbers pm and rank positive integer prime polynomial problem proof of Theorem prove quadratic rational canonical form rational functions real numbers result root in F)n satisfying Section sequence sieve similar over F singular solution solvable group subfields of F)n Suppose variables virtually-one-one zero