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ITAMO
2017 ITAMO
5
5
Part of
2017 ITAMO
Problems
(1)
ITAmo 2017, P5
Source: ITAmo 2017
5/5/2017
Let
x
1
,
x
2
,
x
3
.
.
.
x_1 , x_2, x_3 ...
x
1
,
x
2
,
x
3
...
a succession of positive integers such that for every couple of positive integers
(
m
,
n
)
(m,n)
(
m
,
n
)
we have
x
m
n
≠
x
m
(
n
+
1
)
x_{mn} \neq x_{m(n+1)}
x
mn
=
x
m
(
n
+
1
)
. Prove that there exists a positive integer
i
i
i
such that
x
i
≥
2017
x_i \ge 2017
x
i
≥
2017
.
number theory
algebra
Ramsey Theory
combinatorics