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A. I. Vinogradov Acta Arith admissible mod admissible polynomials AH CCCP algebraic number algebraic number field application arbitrary arithmetic progression assume asymptotic formula Bcex Behrens-Fisher problem choose condition congruence constant coprime Corollary correspondence defined definition denote the number diophantine equation Dirichlet divisors Dokl ecjiH English transl equivalent ergodic method estimate exists follows function Hence hermitions hjih hypothesis ideals Ilycmb implies inequality JIemma JJokji Lemma Linnik Lucas sequences MaTeM matrix meopuu MocKBa mod q natural numbers norm npocTbix number of solutions number theory obtain p-adic Pell equation positive integers prime ideals prime number primitive integral problem proof of Theorem prove quadratic residue quaternions real numbers representation result satisfying Satz sequence soluble Soviet Math square-free square-free integers sufficiently large Suppose Teopema TeopeMbi ternary quadratic forms values vectors whence xoth XXVII Ycnexn ypaBHeHHH zeros