IMO Shortlist 2003 problem N7
Avg:
Avg:
The sequence
,
,
is defined as follows:
for
. Prove that if an odd prime
divides
, then
divides
.
comment
Hi guys ,
Here is a nice problem:
Let be given a sequence
such that
and
. Show that if
is an odd prime such that
then we have 
Here are some futher question proposed by me :Prove or disprove that :
1)
2) for every odd prime number
we have
where
where
or 
Thanks kiu si u
Edited by Orl.










comment
Hi guys ,
Here is a nice problem:
Let be given a sequence






Here are some futher question proposed by me :Prove or disprove that :
1)

2) for every odd prime number





Thanks kiu si u
Edited by Orl.
Izvor: Međunarodna matematička olimpijada, shortlist 2003