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National and Regional Contests
PEN Problems
PEN N Problems
16
16
Part of
PEN N Problems
Problems
(1)
N 16
Source:
5/25/2007
Does there exist positive integers
a
1
<
a
2
<
⋯
<
a
100
a_{1}<a_{2}<\cdots<a_{100}
a
1
<
a
2
<
⋯
<
a
100
such that for
2
≤
k
≤
100
2 \le k \le 100
2
≤
k
≤
100
, the greatest common divisor of
a
k
−
1
a_{k-1}
a
k
−
1
and
a
k
a_{k}
a
k
is greater than the greatest common divisor of
a
k
a_{k}
a
k
and
a
k
+
1
a_{k+1}
a
k
+
1
?
greatest common divisor
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