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- Publisher Website: 10.1016/0022-314X(82)90022-1
- Scopus: eid_2-s2.0-49049141648
- WOS: WOS:A1982PN98100002
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Article: Diophantine inequalities with mixed powers
Title | Diophantine inequalities with mixed powers |
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Authors | |
Issue Date | 1982 |
Publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/jnt |
Citation | Journal Of Number Theory, 1982, v. 15 n. 2, p. 149-163 How to Cite? |
Abstract | Let {λi}i = 1 s (s ≥ 2) be a finite sequence of non-zero real numbers, not all of the same sign and in which not all the ratios λi λj are rational. A given sequence of positive integers {ni}i = 1 s is said to have property (P) ((P*) respectively) if for any {λi}i = 1 s and any real number η, there exists a positive constant σ, depending on {λi}i = 1 s and {ni}i = 1 s only, so that the inequality |η + Σi = 1 s λixi ni| < (max xi)-σ has infinitely many solutions in positive integers (primes respectively) x1, x2,..., xs. In this paper, we prove the following result: Given a sequence of positive integers {ni}i = 1 ∞, a necessary and sufficient condition that, for any positive integer j, there exists an integer s, depending on {ni}i = j ∞ only, such that {ni}i = j j + s - 1 has property (P) (or (P*)), is that Σi = 1 ∞ ni -1 = ∞. These are parallel to some striking results of G. A. Freǐman, E. J. Scourfield and K. Thanigasalam. © 1982. |
Persistent Identifier | http://hdl.handle.net/10722/156228 |
ISSN | 2023 Impact Factor: 0.6 2023 SCImago Journal Rankings: 0.780 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Tsang, KM | en_US |
dc.date.accessioned | 2012-08-08T08:40:55Z | - |
dc.date.available | 2012-08-08T08:40:55Z | - |
dc.date.issued | 1982 | en_US |
dc.identifier.citation | Journal Of Number Theory, 1982, v. 15 n. 2, p. 149-163 | en_US |
dc.identifier.issn | 0022-314X | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/156228 | - |
dc.description.abstract | Let {λi}i = 1 s (s ≥ 2) be a finite sequence of non-zero real numbers, not all of the same sign and in which not all the ratios λi λj are rational. A given sequence of positive integers {ni}i = 1 s is said to have property (P) ((P*) respectively) if for any {λi}i = 1 s and any real number η, there exists a positive constant σ, depending on {λi}i = 1 s and {ni}i = 1 s only, so that the inequality |η + Σi = 1 s λixi ni| < (max xi)-σ has infinitely many solutions in positive integers (primes respectively) x1, x2,..., xs. In this paper, we prove the following result: Given a sequence of positive integers {ni}i = 1 ∞, a necessary and sufficient condition that, for any positive integer j, there exists an integer s, depending on {ni}i = j ∞ only, such that {ni}i = j j + s - 1 has property (P) (or (P*)), is that Σi = 1 ∞ ni -1 = ∞. These are parallel to some striking results of G. A. Freǐman, E. J. Scourfield and K. Thanigasalam. © 1982. | en_US |
dc.language | eng | en_US |
dc.publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/jnt | en_US |
dc.relation.ispartof | Journal of Number Theory | en_US |
dc.title | Diophantine inequalities with mixed powers | en_US |
dc.type | Article | en_US |
dc.identifier.email | Tsang, KM:kmtsang@maths.hku.hk | en_US |
dc.identifier.authority | Tsang, KM=rp00793 | en_US |
dc.description.nature | link_to_subscribed_fulltext | en_US |
dc.identifier.doi | 10.1016/0022-314X(82)90022-1 | - |
dc.identifier.scopus | eid_2-s2.0-49049141648 | en_US |
dc.identifier.volume | 15 | en_US |
dc.identifier.issue | 2 | en_US |
dc.identifier.spage | 149 | en_US |
dc.identifier.epage | 163 | en_US |
dc.identifier.isi | WOS:A1982PN98100002 | - |
dc.publisher.place | United States | en_US |
dc.identifier.scopusauthorid | Tsang, KM=7201554731 | en_US |
dc.identifier.issnl | 0022-314X | - |