Midy's theorem in non-integer bases and divisibility of Fibonacci numbers

DOI10.46298/CM.12840MaRDI QIDQ6615624

Zuzana Masáková, Edita Pelantová

Publication date: 8 October 2024

Published in: Communications in Mathematics (Search for Journal in Brave)

zbMATH Keywords

Fibonacci numbers\(\beta\)-expansionsMidy theorem

Mathematics Subject Classification ID

Radix representation; digital problems (11A63) Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. (11K16) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Cites Work

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• History of the theory of numbers. Vol. I: Divisibility and primality. Vol. II: Diophantine analysis. Vol. III: Quadratic and higher forms.
• The Period, Rank, and Order of the (a, b)-Fibonacci Sequence Mod m
• Repeating Decimals: A Period Piece
• Representations for real numbers and their ergodic properties
• On theβ-expansions of real numbers
• Rational numbers with purely periodic β -expansion
• On Periodic Expansions of Pisot Numbers and Salem Numbers
• Complementary Rational Numbers
• A Theorem on Repeating Decimals

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