| Autors: Dimitrov, S. I. Title: Diophantine approximation with one prime of the form p=x^2+y^2+1 Keywords: diophantine approximation, primes Abstract: Let ε>0 be a small constant. In the present paper we prove that whenever η is real and constants λ_i satisfy some necessary conditions, then there exist infinitely many prime triples p_1, p_2, p_3 satisfying the inequality |λ_1 p_1 + λ _2 p_2 + λ_3 p_3+η|< ε and such that p_3=x^2 + y^2 +1. References Issue
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Цитирания (Citation/s):
1. Li X., Ge W., A Diophantine approximation problem with unlike powers of primes, 2025, AIMS Mathematics, issue 1, vol. 10, pp. 736-753, DOI 10.3934/math.2025034, eissn 24736988 - 2025 - в издания, индексирани в Scopus
2. Hu L., Liu F., Liu S., An equation involving prime numbers and one Linnik prime, 2025, Ramanujan Journal, issue 3, vol. 67, DOI 10.1007/s11139-025-01114-6, issn 13824090, eissn 15729303 - 2025 - в издания, индексирани в Scopus
3. Liu Y., On a Diophantine equation involving one Linnik prime, 2025, Ramanujan Journal, issue 2, vol. 68, DOI 10.1007/s11139-025-01191-7, issn 13824090, eissn 15729303 - 2025 - в издания, индексирани в Scopus
4. Todorova T.L., Georgieva A., A Diophantine Inequality Involving Mixed Powers of Primes with a Specific Type, 2025, Mathematics, issue 19, vol. 13, DOI 10.3390/math13193065, eissn 22277390 - 2025 - в издания, индексирани в Scopus
5. H. Liu, R. Liu, On the exceptional set for Diophantine inequality with unlike powers of primes, Lith. Math. J. (ISSN : 0363-1672 (print), ISSN : 1573-8825 (online)), vol. 64, 1, (2024), 34 -- 52, (https://doi.org/10.1007/s10986-024-09624-4). - 2024 - в издания, индексирани в Scopus и/или Web of Science
6. Liu Y., On a ternary Diophantine inequality with one prime of the form p=x2+y2+1, 2025, Ramanujan Journal, issue 1, vol. 66, pp. 1-16, DOI 10.1007/s11139-024-00986-4, issn 13824090, eissn 15729303 - 2025 - в издания, индексирани в Scopus
Вид: пленарен доклад в международен форум, публикация в издание с импакт фактор, индексирана в Scopus