A NOTE ON SOME DIOPHANTINE EQUATIONS

Keskin, Refik; Merve Guney Duman

dc.contributor.authors	Keskin, R; Duman, MG;
dc.date.accessioned	2020-01-17T08:21:41Z
dc.date.available	2020-01-17T08:21:41Z
dc.date.issued	2017
dc.identifier.citation	Keskin, R; Duman, MG; (2017). A NOTE ON SOME DIOPHANTINE EQUATIONS. MISKOLC MATHEMATICAL NOTES, 18, 249-235
dc.identifier.issn	1787-2405
dc.identifier.uri	https://hdl.handle.net/20.500.12619/6088
dc.identifier.uri	https://doi.org/10.18514/MMN.2017.1857
dc.description.abstract	Let k >= 3 be an odd integer. In this paper we investigate all positive integer solutions of the equations x(4) - kx(2) y + y(2) = -/+ A, x(4) kx(2) y + y(2) = -/+ A(k(2) - 4), x(4) - (k(2) - 4)y(2) = -/+ 4A, and x(2) - (k(2) - 4)y(4) = -/+ 4A with A = -/+(k -/+ 2). We show that if k = 1(mod8) and k(2) - 4 be a square-free integer; then the equation x(4) - kx(2) y + y(2) = (k - 2)(k(2) - 4) has no positive integer solutions. Moreover, if k(2) - 4 be a square-free integer; then the equation x(4) - kx(2) y + y(2) = -(k + 2)(k(2) - 4) has no positive integer solutions.
dc.language	English
dc.publisher	UNIV MISKOLC INST MATH
dc.subject	Mathematics
dc.title	A NOTE ON SOME DIOPHANTINE EQUATIONS
dc.type	Article
dc.identifier.volume	18
dc.identifier.startpage	235
dc.identifier.endpage	249
dc.contributor.department	Sakarya Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü
dc.contributor.saüauthor	Keskin, Refik
dc.relation.journal	MISKOLC MATHEMATICAL NOTES
dc.identifier.wos	WOS:000406745600021
dc.identifier.doi	10.18514/MMN.2017.1857
dc.identifier.eissn	1787-2413
dc.contributor.author	Keskin, Refik
dc.contributor.author	Merve Guney Duman