Algebraic Divisibility Sequences over Function Fields
نویسندگان
چکیده
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. In Memory of Alf van der Poorten, Mathematician, Colleague, Friend
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