2023-11-012023-11-012018Çelik, G. S. ve Soydan, G. (2018). ''Elliptic curves containing sequences of consecutive cubes''. Rocky Mountain Journal of Mathematics, 48(7), 2163-2174.0035-75961945-3795https://doi.org/10.1216/RMJ-2018-48-7-2163https://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-48/issue-7/Elliptic-curves-containing-sequences-of-consecutive-cubes/10.1216/RMJ-2018-48-7-2163.fullhttp://hdl.handle.net/11452/34732Let E be an elliptic curve over Q described by y(2) = x(3)+Kx+L, where K, L is an element of Q. A set of rational points (x(i), y(i)) is an element of E(Q) for i = 1, 2,..., k, is said to be a sequence of consecutive cubes on E if the x-coordinates of the points x(i)'s for i = 1, 2,..., form consecutive cubes. In this note, we show the existence of an infinite family of elliptic curves containing a length-5-term sequence of consecutive cubes. Moreover, these five rational points in E(Q) are linearly independent, and the rank r of E(Q) is at least 5.eninfo:eu-repo/semantics/openAccessMathematicsElliptic curvesRational pointsSequences of consecutive cubesArithmetic progressionsArticle0004532271000032-s2.0-8506162785321632174487MathematicsRank Of Data; Congruent Numbers; Selmer Group