Journal of Integer Sequences, Vol. 26 (2023), Article 23.3.8

Jakóbczyk's Hypothesis on Mersenne Numbers and Generalizations of Skula's Theorem

Jiří Klaška
Institute of Mathematics
Faculty of Mechanical Engineering
Brno University of Technology
Technická 2
CZ — 616 69 Brno
Czech Republic


Recently Skula published an interesting article on the divisibility of Mersenne numbers 2n – 1 by powers of primes. His main result is closely related to Jakóbczyk's hypothesis. We generalize Skula's result for the numbers an ± 1 where aN, a ≥ 2.

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(Concerned with sequences A000215 A000225 A001220 A077816.)

Received February 9 2023; revised versions received March 16 2023; March 17 2023. Published in Journal of Integer Sequences, March 17 2023.

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