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Mathematics of Computation

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Primitive divisors of Lucas and Lehmer sequences

Author: Paul M. Voutier
Journal: Math. Comp. 64 (1995), 869-888
MSC: Primary 11D61; Secondary 11B39, 11Y50
MathSciNet review: 1284673
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Abstract: Stewart reduced the problem of determining all Lucas and Lehmer sequences whose nth 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 \leq 30$. Further computations lead us to conjecture that, for $ n > 30$, the nth element of such sequences always has a primitive divisor.

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Keywords: Lucas sequences, Lehmer sequences, primitive divisors, Thue equations
Article copyright: © Copyright 1995 American Mathematical Society

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