IMO Shortlist 1994 problem N6


Kvaliteta:
  Avg: 0,0
Težina:
  Avg: 8,0
Dodao/la: arhiva
2. travnja 2012.
LaTeX PDF
Define the sequence a_1, a_2, a_3, ... as follows. a_1 and a_2 are coprime positive integers and a_{n + 2} = a_{n + 1}a_n + 1. Show that for every m > 1 there is an n > m such that a_m^m divides a_n^n. Is it true that a_1 must divide a_n^n for some n > 1?
Izvor: Međunarodna matematička olimpijada, shortlist 1994