A note on the Fibonacci $m$-step sequences modulo $q$
Abstract
We briefly discuss a congruence relation on the subsequence of the Fibonacci $m$-step numbers. Then we use the obtained result to establish many identities regarding the Tribonacci numbers mod $q$ with indices in arithmetic progression and connect them with the existing results. Finally, we discuss arbitrary linear recurrence sequences.Keywords
Fibonacci $m$-step numbers, Tribonacci numbers, linear recurrence, Pisano number, congruence