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Application of theorems on primes to diophantine problems of a special type

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Abstract

In this paper we consider the problem of whether the equation

$$\begin{array}{*{20}c} {n\frac{{v_1 \varphi _1 - v_2 \varphi _2 }}{{v_1 - v_2 }}} & {v_1 \ne v_2 } \\ \end{array} $$

can be solved and of a lower bound for the number of solutions,subject to certain constraints on the density of the numbers ν and the distribution of the numbers ϕ in arithmetic progressions.

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Literature cited

  1. I. M. Vinogradov, Collected Works [in Russian], Moscow (1952).

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  3. A. I. Vinogradov,“Numbers with small prime divisors,” Dokl. Akad. Nauk, SSSR,109, No. 4, 683–686 (1956).

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Authors and Affiliations

  1. Leningrad Branch of the V. A. Steklov Mathematical Institute, Academy of Sciences of the USSR, USSR

    B. M. Bredikhin & Yu. V. Linnik

Authors
  1. B. M. Bredikhin
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  2. Yu. V. Linnik
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Additional information

Deceased.

Translated from Matematicheskie Zametki, Vol. 12, No. 3, pp. 243–250, September, 1972.

In conclusion the authors wish to express their deep gratitude to S. Utiyam for discussing the paper and for valuable observations on it.

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Bredikhin, B.M., Linnik, Y.V. Application of theorems on primes to diophantine problems of a special type. Mathematical Notes of the Academy of Sciences of the USSR 12, 580–584 (1972). https://doi.org/10.1007/BF01093988

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  • DOI: https://doi.org/10.1007/BF01093988

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