CONCORDANT NUMBERS WITHIN ARITHMETIC PROGRESSIONS AND ELLIPTIC CURVES

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dc.contributor.authorIm, Bo-Haeko
dc.date.accessioned2016-09-08T00:51:37Z-
dc.date.available2016-09-08T00:51:37Z-
dc.date.created2016-09-07-
dc.date.created2016-09-07-
dc.date.issued2013-03-
dc.identifier.citationPROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, v.141, no.3, pp.791 - 800-
dc.identifier.issn0002-9939-
dc.identifier.urihttp://hdl.handle.net/10203/212935-
dc.description.abstractIf the system of two diophantine equations X-2 + mY(2) = Z(2) and X-2 + nY(2) = W-2 has infinitely many integer solutions (X, Y, Z, W) with gcd(X, Y) = 1, equivalently, the elliptic curve E-m,E-n : y(2) = x(x + m)(x + n) has positive rank over Q, then (m, n) is called a strongly concordant pair. We prove that for a given positive integer M and an integer k, the number of strongly concordant pairs (m, n) with m, n is an element of [1, N] and m, n equivalent to k is at least O(N), and we give a parametrization of them-
dc.languageEnglish-
dc.publisherAMER MATHEMATICAL SOC-
dc.subjectFORMS-
dc.titleCONCORDANT NUMBERS WITHIN ARITHMETIC PROGRESSIONS AND ELLIPTIC CURVES-
dc.typeArticle-
dc.identifier.wosid000326516700007-
dc.identifier.scopusid2-s2.0-84871697611-
dc.type.rimsART-
dc.citation.volume141-
dc.citation.issue3-
dc.citation.beginningpage791-
dc.citation.endingpage800-
dc.citation.publicationnamePROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY-
dc.identifier.doi10.1090/S0002-9939-2012-11372-3-
dc.contributor.localauthorIm, Bo-Hae-
dc.type.journalArticleArticle-
dc.subject.keywordPlusFORMS-
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