## Algebraic Divisibility Sequences Over Function Fields

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.

Published in:
Journal Of The Australian Mathematical Society, 92, 1, 99-126
Year:
2012
Publisher:
New York, Australian Mathematical Society
ISSN:
1446-7887
Keywords:
Laboratories: