In this Thesis the identity of k-Tribonacci numbers in modular ring Z6 and in modular ring Z8 are discussed and their relationship with the k-Tribonacci number of factors of 6 and the factor of 8 are analysed using the method carried out by Layendekkers and Shannon [Notes on Number Theory and Discrete Mathematics, 19 (2013), 66-72]. Our computational experiment results show that (i) for k ≡ 1…