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Czech-Polish-Slovak Match
1999 Czech and Slovak Match
4
4
Part of
1999 Czech and Slovak Match
Problems
(1)
Find All k
Source: Czech and Slovak Match 1999
7/28/2006
Find all positive integers
k
k
k
for which the following assertion holds: If
F
(
x
)
F(x)
F
(
x
)
is polynomial with integer coefficients ehich satisfies
F
(
c
)
≤
k
F(c) \leq k
F
(
c
)
≤
k
for all
c
∈
{
0
,
1
,
⋯
,
k
+
1
}
c \in \{0,1, \cdots,k+1 \}
c
∈
{
0
,
1
,
⋯
,
k
+
1
}
, then
F
(
0
)
=
F
(
1
)
=
⋯
=
F
(
k
+
1
)
.
F(0)= F(1) = \cdots =F(k+1).
F
(
0
)
=
F
(
1
)
=
⋯
=
F
(
k
+
1
)
.
algebra
polynomial
algebra proposed