Prempreesuk, Noppakaew, and Pongsriiam determined the Zeckendorf representation of the multiplicative inverse of 2 modulo F-n, for every positive integer n not divisible by 3, where F-n denotes the nth Fibonacci number. We determine the Zeckendorf representation of the multiplicative inverse of a modulo F-n, for every fixed integer a >= 3 and for all positive integers n with gcd(a, F-n) = 1. Our proof makes use of the so-called base-phi expansion of real numbers.

Zeckendorf representation of multiplicative inverses modulo a Fibonacci number / Alecci, Gessica; Murru, Nadir; Sanna, Carlo. - In: MONATSHEFTE FÜR MATHEMATIK. - ISSN 0026-9255. - 201:1(2023), pp. 1-9. [10.1007/s00605-022-01724-y]

Zeckendorf representation of multiplicative inverses modulo a Fibonacci number

Murru, Nadir
;
2023-01-01

Abstract

Prempreesuk, Noppakaew, and Pongsriiam determined the Zeckendorf representation of the multiplicative inverse of 2 modulo F-n, for every positive integer n not divisible by 3, where F-n denotes the nth Fibonacci number. We determine the Zeckendorf representation of the multiplicative inverse of a modulo F-n, for every fixed integer a >= 3 and for all positive integers n with gcd(a, F-n) = 1. Our proof makes use of the so-called base-phi expansion of real numbers.
2023
1
Alecci, Gessica; Murru, Nadir; Sanna, Carlo
Zeckendorf representation of multiplicative inverses modulo a Fibonacci number / Alecci, Gessica; Murru, Nadir; Sanna, Carlo. - In: MONATSHEFTE FÜR MATHEMATIK. - ISSN 0026-9255. - 201:1(2023), pp. 1-9. [10.1007/s00605-022-01724-y]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/351100
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