Prime numbers are the most important numbers in number theory and cryptography. One of such special primes are given by the set of Mersenne primes, that are derived from the form Mn = 2n − 1, where n is a prime number. In this paper, we examine the appearance of these primes in certain sequences of Lucas numbers of the first kind Un (P, Q) or the second kind Vn (P, Q). Namely, we completely solve the Diophantine equation Mn = Un (P, Q) or Mn = Vn (P, Q) for certain nonzero relatively prime parameters P and Q.
Hadi et al. (Wed,) studied this question.
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