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Erdős Problem #276 — Is it possible for a Lucas sequence to have all terms composite without\textit{without} having an underlying system of covering congruences responsible?

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Is it possible for a Lucas sequence to have all terms composite without\textit{without} having an underlying system of covering congruences responsible? (In other words, no positive integer has a common factor with every term of the sequence).

References

Primary source

Erdős, P. and Graham, R., Old and new problems and results in combinatorial number theory. Monographies de L'Enseignement Mathématique 28 (1980).

Additional references

Erdős, P. and Graham, R., Old and new problems and results in combinatorial number theory. Monographies de L'Enseignement Mathématique 28 (1980).

covering-systemsnumber-theory
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