We study generalized Fibonacci sequences with initial values and . Let be relatively prime nonzero integers such that is not a perfect square. We show that if then the sequence misses a congruence class modulo every large enough prime. If , we prove under the GRH that the sequence hits every congruence class modulo infinitely many primes.
"Complete generalized Fibonacci sequences modulo primes." Mosc. J. Comb. Number Theory 9 (1) 1 - 15, 2020. https://doi.org/10.2140/moscow.2020.9.1