Irmak, NurettinAlp, Murat2024-11-072024-11-0720171787-24051787-2413https://doi.org/10.18514/MMN.2017.2131https://hdl.handle.net/11480/15072In this paper, we show that there is no solution of the diophantine equation u(1)(k) + u(2)(k) + . . . + u(n+1)(l) + u(n+2)(l) + . . . + u(n+r)(l) for special cases of k and l where the elements of sequence {u(n)} satisfy the relation u(n) = Aun-1 - u(n-2) with u(0) = 0, u(1) = 1 and A >= 3 is a positive integer.eninfo:eu-repo/semantics/openAccessDiophantine equationLucas sequenceArticle18285185810.18514/MMN.2017.21312-s2.0-85116361496Q3WOS:000425348300025Q3