Distribution of Residues of Certain Second-Order Linear Recurrences Modulo P

Lawrence Somer

A chapter in Applications of Fibonacci Numbers, 1990, pp 311-324 from Springer

Abstract: Abstract Let (w) = w(a, b) be a second-order linear recurrence defined by the relation (1) $${w_{n + 2}} = a{w_{n + 1}} + b{w_n},$$ where the parameters a and b and the initial terms w0, w1 are all integers. Let D = a2 + 4b be the discriminant of w(a, b). Let $${x^2} - ax - b$$ be the characteristic polynomial associated with w(a, b) and let r1 and r2 be its characteristic roots. Throughout this paper, p will denote an odd prime unless specified otherwise. Further, d will always denote a residue modulo p. We say that the recurrence (w) is defective modulo p if (w) has an incomplete system of residues modulo p.

Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-1910-5_34

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DOI: 10.1007/978-94-009-1910-5_34

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