Irmak, NurettinSzalay, Laszlo2024-11-072024-11-0720191406-22832228-4699https://doi.org/10.12697/ACUTM.2019.23.06https://hdl.handle.net/11480/15070Let L-m denote the m(th) Lucas number. We show that the solutions to the diophantine equation ((2t)(k)) = L-m, in non-negative integers t, k <= 2(t-1), and m, are (t, k, m) = (1, 1, 0), (2,1, 3), and (a, 0,1) with non-negative integers a.eninfo:eu-repo/semantics/openAccessLucas numberbinomial coefficientdiophantine equationArticle231657010.12697/ACUTM.2019.23.062-s2.0-85073285209Q4WOS:000481498100006N/A