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Cyclotomic polynomials play fundamental roles in number theory, combinatorics, algebra and their applications. Hence their properties have been extensively investigated. In this paper, we study the maximum gap g (maximum of the differences between any two consecutive exponents). In 2012, it was shown that g (Φp 1 p 2 ) = p1 − 1 for primes p2 > p1. In 2017, based on numerous calculations, the following generalization was conjectured: g (Φmp) = ϕ(m) for square free odd m and prime p > m. The main contribution of this paper is a proof of this conjecture.

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In this note, we prove that there is no number with the Lehmer property in the sequences of Jaconsthsl or Jacobsthal-Lucas numbers.