Journal of Integer Sequences, Vol. 25 (2022), Article 22.9.4

Generalization of Greatest Common Divisor of Shifted Fibonacci Numbers

Tran Quang Do and Luu Ba Thang
Department of Mathematics and Informatics
Hanoi National University of Education
136 Xuan Thuy
Cau Giay


Let Fn denote the n'th Fibonacci number and let k be a positive integer. We find necessary and sufficient conditions on s and t so that the function n → gcd(Fn + s, Fn + k + t) is unbounded.

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(Concerned with sequences A000045 A000204.)

Received October 18 2022; revised versions received November 8 2022; November 11 2022. Published in Journal of Integer Sequences, November 13 2022.

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