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Problems
Contests
National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2018 India PRMO
30
30
Part of
2018 India PRMO
Problems
(1)
2018 preRMO p30 integer P(x), P(1) = 4 and P(5) = 136, P(3) ?
Source:
8/8/2019
Let
P
(
x
)
P(x)
P
(
x
)
=
a
0
+
a
1
x
+
a
2
x
2
+
⋯
+
a
n
x
n
a_0+a_1x+a_2x^2+\cdots +a_nx^n
a
0
+
a
1
x
+
a
2
x
2
+
⋯
+
a
n
x
n
be a polynomial in which
a
i
a_i
a
i
is non-negative integer for each
i
∈
i \in
i
∈
{
0
,
1
,
2
,
3
,
.
.
.
.
,
n
0,1,2,3,....,n
0
,
1
,
2
,
3
,
....
,
n
} . If
P
(
1
)
=
4
P(1) = 4
P
(
1
)
=
4
and
P
(
5
)
=
136
P(5) = 136
P
(
5
)
=
136
, what is the value of
P
(
3
)
P(3)
P
(
3
)
?
polynomial
algebra