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Malaysia Contests
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JOM 2015
4
4
Part of
JOM 2015
Problems
(1)
Strictly Increasing Sequences
Source: Junior Olympiad of Malaysia Shortlist 2015 N3 (JOM P4)
7/17/2015
Given a natural number
n
≥
3
n\ge 3
n
≥
3
, determine all strictly increasing sequences
a
1
<
a
2
<
⋯
<
a
n
a_1<a_2<\cdots<a_n
a
1
<
a
2
<
⋯
<
a
n
such that
gcd
(
a
1
,
a
2
)
=
1
\text{gcd}(a_1,a_2)=1
gcd
(
a
1
,
a
2
)
=
1
and for any pair of natural numbers
(
k
,
m
)
(k,m)
(
k
,
m
)
satisfy
n
≥
m
≥
3
n\ge m\ge 3
n
≥
m
≥
3
,
m
≥
k
m\ge k
m
≥
k
,
a
1
+
a
2
+
⋯
+
a
m
a
k
\frac{a_1+a_2+\cdots +a_m}{a_k}
a
k
a
1
+
a
2
+
⋯
+
a
m
is a positive integer.
number theory