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MathLinks Contest 6th
2.2
2.2
Part of
MathLinks Contest 6th
Problems
(1)
0622 number theory with combinations 6th edition Round 2 p2
Source:
5/3/2021
Let
a
1
,
a
2
,
.
.
.
,
a
n
−
1
a_1, a_2, ..., a_{n-1}
a
1
,
a
2
,
...
,
a
n
−
1
be
n
−
1
n - 1
n
−
1
consecutive positive integers in increasing order such that
k
k
k
(
n
k
)
{n \choose k}
(
k
n
)
≡
0
\equiv 0
≡
0
(mod
a
k
a_k
a
k
), for all
k
∈
{
1
,
2
,
.
.
.
,
n
−
1
}
k \in \{1, 2, ... , n - 1\}
k
∈
{
1
,
2
,
...
,
n
−
1
}
. Find the possible values of
a
1
a_1
a
1
.
number theory
Combinations
6th edition