Vol. 118, No. 2, 1985

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ISSN: 0030-8730
The set of primes dividing the Lucas numbers has density 23

Jeffrey C. Lagarias

Vol. 118 (1985), No. 2, 449–461
Abstract

The Lucas numbers Ln are defined by L0 = 2, L1 = 1 and the recurrence Ln = Ln1 + Ln2. The set of primes SL = {p : p divides Ln for some n} has density 2/3. Similar density results are proved for sets of primes SU = {p : p divides Un for some n} for certain other special second-order linear recurrences {Un}. The proofs use a method of Hasse.

Mathematical Subject Classification 2000
Primary: 11B05
Secondary: 11B39
Milestones
Received: 12 September 1984
Revised: 28 September 1984
Published: 1 June 1985
Authors
Jeffrey C. Lagarias
University of Michigan
United States