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Austrian-Polish
1981 Austrian-Polish Competition
1
1
Part of
1981 Austrian-Polish Competition
Problems
(1)
Set and smalles integer
Source: Austrain- Polish competition 1981
12/7/2013
Find the smallest
n
n
n
for which we can find
15
15
15
distinct elements
a
1
,
a
2
,
.
.
.
,
a
15
a_{1},a_{2},...,a_{15}
a
1
,
a
2
,
...
,
a
15
of
{
16
,
17
,
.
.
.
,
n
}
\{16,17,...,n\}
{
16
,
17
,
...
,
n
}
such that
a
k
a_{k}
a
k
is a multiple of
k
k
k
.
number theory unsolved
number theory