A Congruent Property of Gibonacci Number Modulo Prime

Let a, b ∈ Z and p be a prime number such that are not divisible by p. In this work, we give congruent property modulo of the gibonacci defined Gn = Gn−1 + Gn−2 with initial condition G1 G2 b. We show sequence satisfying Gkp−(p/5) ≡ Gk−1 (mod p) for all positive integer k odd ≠ 5 if only p). Moreover, each p, necessary sufficient yielding also find relation between sequences in same equivalent class constructed Aoki Sakai [1] leads to property.