Denote by $F_n$ the $n^{\text{th}}$ Fibonacci number $(F_1=F_2=1)$.Prove that if $a,b,c$ are positive integers such that $a| F_b,b|F_c,c|F_a$,then either $5$ divides each of $a,b,c$ or $12$ divides each of $a,b,c$.
Problem
Source: India Postal Coaching 2014 Set 4 Problem 4
Tags: number theory unsolved, number theory
29.11.2014 13:39
Here is a solution in Hungarian : http://www.komal.hu/verseny/feladat.cgi?a=feladat&f=A598&l=en
16.06.2017 19:11
Who can translate it into English
16.06.2017 19:22
There is a button that says "translate to english". Press it, and you can mostly understand its contents. Alternatively, go to this link: http://translate.google.com/translate?js=n&sl=hu&tl=en&u=https://www.komal.hu/verseny/feladat.cgi%3Fa%3Dfeladat%26f%3DA598%26l%3Den
16.06.2017 19:24
In china we can't use Google Translation
16.06.2017 19:33
Well then... I'll c/p it in:
Sorry, the notation sucks. Look back to the website if you need to clarify any symbols.
16.06.2017 19:37
Thank you very much