Publication: Mersenne numbers as a difference of two Lucas numbers
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CHARLES UNIV, FAC MATHEMATICS & PHYSICS
DOI
10.14712/1213-7243.2022.027
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Abstract
Let (L-n)(n >= 0) be the Lucas sequence. We show that the Diophantine equation L-n - L-m = M-k has only the nonnegative integer solutions (n, m, k) = (2, 0, 1), (3, 1, 2), (3, 2, 1), (4, 3, 2), (5, 3, 3), (6, 2, 4), (6, 5, 3) where M-k = 2(k) - 1 is the kth Mersenne number and n > m.
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COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE
ISSN
0010-2628
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openAccess