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Mat. Zametki, 1972, Volume 12, Issue 3, Pages 243–250 (Mi mz9874)  

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

B. M. Bredikhin, Yu. V. Linnik

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

Abstract: In this paper we consider the problem of whether the equation
$$ n=\frac{\nu_1\varphi_1-\nu_2\varphi_2}{\nu_1-\nu_2}\qquad (\nu_1\ne\nu_2) $$
can be solved and of a lower bound for the number of solutions, subject to certain constraints on the density of the numbers $\nu$ and the distribution of the numbers $\varphi$ in arithmetic progressions.

Full text: PDF file (820 kB)

English version:
Mathematical Notes, 1972, 12:3, 580–584

Bibliographic databases:

UDC: 511
Received: 23.11.1971

Citation: B. M. Bredikhin, Yu. V. Linnik, “Application of theorems on primes to diophantine problems of a special type”, Mat. Zametki, 12:3 (1972), 243–250; Math. Notes, 12:3 (1972), 580–584

Citation in format AMSBIB
\Bibitem{BreLin72}
\by B.~M.~Bredikhin, Yu.~V.~Linnik
\paper Application of theorems on primes to diophantine problems of a special type
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 3
\pages 243--250
\mathnet{http://mi.mathnet.ru/mz9874}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=318078}
\zmath{https://zbmath.org/?q=an:0247.10011}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 3
\pages 580--584
\crossref{https://doi.org/10.1007/BF01093988}


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