Gueye, AliouneRıhane, Salah EddineTogb, Alain2025-01-062025-01-0620211300-00981303-614910.3906/mat-2106-86https://doi.org/10.3906/mat-2106-86https://search.trdizin.gov.tr/tr/yayin/detay/528511https://hdl.handle.net/20.500.14669/797For k ? 2, consider the k -Fibonacci sequence (F(k)\rn )n?2?k having initial conditions 0, . . . , 0, 1 (k terms)\rand each term afterwards is the sum of the preceding k terms. Some well-known sequences are special cases of this\rgeneralization. The Fibonacci sequence is a special case of (F(k)\rn )n?2?k with k = 2 and Tribonacci sequence is\r(F(k)\rn )n?2?k with k = 3. In this paper, we use Baker’s method to show that 4, 16, 64, 208, 976, and 1936 are all\rk -Fibonacci numbers of the form (3a ± 1)(3b ± 1), where a and b are nonnegative integerseninfo:eu-repo/semantics/openAccessArticle26776266452851145