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Iran MO (3rd Round)
2002 Iran MO (3rd Round)
3
3
Part of
2002 Iran MO (3rd Round)
Problems
(1)
a_n is integer
Source: Iranian National Olympiad (3rd Round) 2002
10/1/2006
a
n
a_{n}
a
n
is a sequence that
a
1
=
1
,
a
2
=
2
,
a
3
=
3
a_{1}=1,a_{2}=2,a_{3}=3
a
1
=
1
,
a
2
=
2
,
a
3
=
3
, and
a
n
+
1
=
a
n
−
a
n
−
1
+
a
n
2
a
n
−
2
a_{n+1}=a_{n}-a_{n-1}+\frac{a_{n}^{2}}{a_{n-2}}
a
n
+
1
=
a
n
−
a
n
−
1
+
a
n
−
2
a
n
2
Prove that for each natural
n
n
n
,
a
n
a_{n}
a
n
is integer.
number theory proposed
number theory