Primitive divisors of Lucas and Lehmer sequences

Voutier, Paul M.

doi:10.1090/S0025-5718-1995-1284673-6

Primitive divisors of Lucas and Lehmer sequences
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Math. Comp. 64 (1995), 869-888 Request permission

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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