Fibonacci Numbers modulo Cubes of Primes

@inproceedings{Sun2010FibonacciNM,
  title={Fibonacci Numbers modulo Cubes of Primes},
  author={Zhi-Wei Sun},
  year={2010}
}
Let p be an odd prime. It is well known that Fp−( p 5 ) ≡ 0 (mod p), where {Fn}n>0 is the Fibonacci sequence and (−) is the Jacobi symbol. In this paper we show that if p 6= 5 then we may determine Fp−( p 5 ) mod p3 in the following way: