Primes Having an Incomplete System of Residues for a Class of Second-Order Recurrences

Lawrence Somer

A chapter in Applications of Fibonacci Numbers, 1988, pp 113-141 from Springer

Abstract: Abstract Shah [4] and Bruckner [1] showed that if p is a prime and p > 7, then the Fibonacci sequence {Fn} has an incomplete system of residues modulo p. Shah established this result for the cases in which p = 1, 9, 11, or 19 modulo 20, while Bruckner proved the result true for the re ma ini n g c ases in which p = 3 or 7 modulo 10. Burr [2] extended these results by dete rmining all the positive integers m for which the Fibonacci sequence has an incomplete system of residues modulo m.

Date: 1988
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DOI: 10.1007/978-94-015-7801-1_12

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