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Romania Team Selection Test
1994 Romania TST for IMO
2:
romania tst
romania tst
Source: Romania TST for IMO 1994,third test
September 6, 2017
algebra
Problem Statement
Let
n
n
n
be a positive integer. Find the number of polynomials
P
(
x
)
P(x)
P
(
x
)
with coefficients in
{
0
,
1
,
2
,
3
}
\{0, 1, 2, 3\}
{
0
,
1
,
2
,
3
}
for which
P
(
2
)
=
n
P(2) = n
P
(
2
)
=
n
.
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