bibkey: jeffery2014divisibility authors: Thomas Jeffery; Rajesh Pereira year: 2014 title: Divisibility Properties of the Fibonacci, Lucas, and Related Sequences doi: 10.1155/2014/750325 url: https://doi.org/10.1155/2014/750325 claim: Proposition 6 proves that each Fibonacci number F_a divides F_am, and Theorem 7 proves that gcd(F_a,F_b) equals F_gcd(a,b). strata_touched: [] license: citation-only triage: anchor

Fibonacci divisibility and gcd laws

Verified locator

Thomas Jeffery and Rajesh Pereira, Divisibility Properties of the Fibonacci, Lucas, and Related Sequences, ISRN Algebra 2014, Article 750325, pages 1–5, DOI 10.1155/2014/750325.

Claim and scope

Proposition 6 states F_a | F_am for positive integers a and m. Theorem 7 states gcd(F_a,F_b)=F_gcd(a,b). Proposition 6 alone implies that, for each positive a and integer divisor d, divisibility of every F_am by d is equivalent to divisibility of F_a by d: one direction uses m=1, and the other uses transitivity.