Prime triples p1, p2, p3 in arithmetic progressions such that p1 = x2 + y2 + 1, p3 = [nc]

S. I. Dimitrov
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 23, 2017, Number 4, Pages 22–33
Full paper (PDF, 225 Kb)

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Authors and affiliations

S. I. Dimitrov
Faculty of Applied Mathematics and Informatics, Technical University of Sofia
8, St. Kliment Ohridski Blvd., 1756 Sofia, Bulgaria

Abstract

In the present paper we prove that there exist infinitely many arithmetic progressions of three different primes p1, p2, p3 = 2p2 − p1 such that p1 = x2 + y2 + 1, p3 = [nc].

Keywords

  • Arithmetic progression
  • Prime numbers
  • Circle method

AMS Classification

  • 11N36
  • 11P32

References

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Cite this paper

Dimitrov, S. I. (2017). Prime Triples p1, p2, p3 in Arithmetic Progressions such that p1 = x2 + y2 + 1, p3 = [nc]. Notes on Number Theory and Discrete Mathematics, 23(4), 22-33.

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