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Published online by Cambridge University Press:  24 April 2012

Department of Mathematics, Colorado State University, Fort Collins, CO 80521, USA (email:
EPF Lausanne, SB-IMB-CSAG, Station 8, CH-1015 Lausanne, Switzerland (email:
Mathematics Department, Brown University, Box 1917, Providence, RI 02912, USA (email:
Department of Mathematics, Stanford University, 450 Serra Mall, Building 380, Stanford, CA 94305, USA (email:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK (email:
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In this note we study the existence of primes and of primitive divisors in function field analogues of classical divisibility sequences. Under various hypotheses, we prove that Lucas sequences and elliptic divisibility sequences over function fields defined over number fields contain infinitely many irreducible elements. We also prove that an elliptic divisibility sequence over a function field has only finitely many terms lacking a primitive divisor.

Research Article
Copyright © Australian Mathematical Publishing Association Inc. 2012


Ingram’s research was supported by a grant from NSERC of Canada. Mahé’s research was supported by the Université de Franche-Comté. Silverman’s research was supported by DMS-0854755. Stange’s research was supported by NSERC PDF-373333 and NSF MSPRF 0802915. Streng’s research was supported by EPSRC grant no. EP/G004870/1.


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