MathDB
Problems
Contests
International Contests
APMO
1995 APMO
5
5
Part of
1995 APMO
Problems
(1)
Function
Source: APMO 1995
3/11/2006
Find the minimum positive integer
k
k
k
such that there exists a function
f
f
f
from the set
Z
\Bbb{Z}
Z
of all integers to
{
1
,
2
,
…
k
}
\{1, 2, \ldots k\}
{
1
,
2
,
…
k
}
with the property that
f
(
x
)
≠
f
(
y
)
f(x) \neq f(y)
f
(
x
)
=
f
(
y
)
whenever
∣
x
−
y
∣
∈
{
5
,
7
,
12
}
|x-y| \in \{5, 7, 12\}
∣
x
−
y
∣
∈
{
5
,
7
,
12
}
.
function
modular arithmetic
algebra unsolved
algebra