A note on the Fibonacci $m$-step sequences modulo $q$

Karol Gryszka


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.


Fibonacci $m$-step numbers, Tribonacci numbers, linear recurrence, Pisano number, congruence

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ISSN: 1331-0623 (Print), 1848-8013 (Online)