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

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## Details

### 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 *p*_{1}, *p*_{2}, *p*_{3} = 2*p*_{2} − *p*_{1} such that *p*_{1} = *x*^{2} + *y*^{2} + 1, *p*_{3} = [*n ^{c}*].

### Keywords

- Arithmetic progression
- Prime numbers
- Circle method

### AMS Classification

- 11N36
- 11P32

### References

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## Cite this paper

APADimitrov, S. I. (2017). Prime Triples *p*_{1}, *p*_{2}, *p*_{3} in Arithmetic Progressions such that *p*_{1} = *x*^{2} + *y*^{2} + 1, *p*_{3} = [*n ^{c}*]. Notes on Number Theory and Discrete Mathematics, 23(4), 22-33.

Dimitrov, S. I. “Prime Triples *p*_{1}, *p*_{2}, *p*_{3} in Arithmetic Progressions such that *p*_{1} = *x*^{2} + *y*^{2} + 1, *p*_{3} = [*n ^{c}*].” Notes on Number Theory and Discrete Mathematics 23, no. 4 (2017): 22-33.

Dimitrov, S. I. “Prime triples *p*_{1}, *p*_{2}, *p*_{3} in arithmetic progressions such that *p*_{1} = *x*^{2} + *y*^{2} + 1, *p*_{3} = [*n ^{c}*].” Notes on Number Theory and Discrete Mathematics 23.4 (2017): 22-33. Print.