Ingram, PatrickMahe, ValerySilverman, Joseph H.Stange, Katherine E.Streng, Marco2013-02-272013-02-272013-02-27201210.1017/S1446788712000092https://infoscience.epfl.ch/handle/20.500.14299/89853WOS:000311400600007In 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.lucas sequenceelliptic divisibility sequenceprimitive divisorfunction field over number fieldtext::journal::journal article::research article