Existence of primitive divisors of Lucas and Lehmer numbers

Yuri Bilu (1) , Guillaume Hanrot (2) , Paul Voutier

1 Mathematisches Institut
2 SPACES - Solving problems through algebraic computation and efficient software

We prove that for~${n>30}$, every~$n$-th Lucas and Lehmer number has a primitive divisor. This allows us to list all Lucas and Lehmer numbers without a primitive divisor.

Mots clés: lucas sequences; primitive divisors; diviseurs primitifs; équations de thue; thue equations; suites de lucas

Domaines: Autre [cs.OH]

Yuri Bilu, Guillaume Hanrot, Paul Voutier. Existence of primitive divisors of Lucas and Lehmer numbers. Journal für die reine und angewandte Mathematik, 2001, 539, pp.75-122. ⟨inria-00100545⟩