Primitive divisors of Lucas and Lehmer sequences

Abstract

Stewart reduced the problem of determining all Lucas and Lehmer sequences whose $n$-th element does not have a primitive divisor to solving certain Thue equations. Using the method of Tzanakis and de Weger for solving Thue equations, we determine such sequences for $n\le 30$. Further computations lead us to conjecture that, for $n>30$, the $n$-th element of such sequences always has a primitive divisor.

References in corpus (1)

• Primitive divisors of Lucas and Lehmer sequences, II

Cited by in corpus (3)

• Primitive divisors of Lucas and Lehmer sequences, III
• Algebraic divisibility sequences over function fields
• On the Diophantine equation N X^2 + 2^L 3^M = Y^N