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International Contests
IMO Longlists
1984 IMO Longlists
46
46
Part of
1984 IMO Longlists
Problems
(1)
Given two sequences. Show that they have finite common terms
Source:
10/12/2010
Let
(
a
n
)
n
≥
1
(a_n)_{n\ge 1}
(
a
n
)
n
≥
1
and
(
b
n
)
n
≥
1
(b_n)_{n\ge 1}
(
b
n
)
n
≥
1
be two sequences of natural numbers such that
a
n
+
1
=
n
a
n
+
1
,
b
n
+
1
=
n
b
n
−
1
a_{n+1} = na_n + 1, b_{n+1} = nb_n - 1
a
n
+
1
=
n
a
n
+
1
,
b
n
+
1
=
n
b
n
−
1
for every
n
≥
1
n\ge 1
n
≥
1
. Show that these two sequences can have only a finite number of terms in common.
number theory unsolved
number theory