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National and Regional Contests
Iran Contests
Iran Team Selection Test
2015 Iran Team Selection Test
1
Easy polynomial
Easy polynomial
Source: Iran TST 2015, first exam, day 1 problem 1
May 17, 2015
algebra
polynomial
algebra proposed
Problem Statement
Find all polynomials
P
,
Q
ā
Q
[
x
]
P,Q\in \Bbb{Q}\left [ x \right ]
P
,
Q
ā
Q
[
x
]
such that
P
(
x
)
3
+
Q
(
x
)
3
=
x
12
+
1.
P(x)^3+Q(x)^3=x^{12}+1.
P
(
x
)
3
+
Q
(
x
)
3
=
x
12
+
1.
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