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Let a_0, a_1, a_2, ... be an infinite sequence of real numbers satisfying the equation a_n=\left|a_{n+1}-a_{n+2}\right| for all n\geq 0, where a_0 and a_1 are two different positive reals.

Can this sequence a_0, a_1, a_2, ... be bounded?

Remark This one is from the IMO Shortlist 2004, but it's already published on the official BWM website und thus I take the freedom to post it here:

Slični zadaci

#NaslovOznakeRj.KvalitetaTežina
2357Mala olimpijada 1996 zadatak 30
2340Hrvatska matematička olimpijada 1994 - Drugi dan - Zadatak 23
2205IMO Shortlist 2006 problem A211
2204IMO Shortlist 2006 problem A117
2122IMO Shortlist 2003 problem A31
2094IMO Shortlist 2002 problem A214