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3
Two-variable polynomial [Iran TST 2010]
Two-variable polynomial [Iran TST 2010]
Source:
June 9, 2010
algebra
polynomial
algebra proposed
Problem Statement
Find all two-variable polynomials
p
(
x
,
y
)
p(x,y)
p
(
x
,
y
)
such that for each
a
,
b
,
c
ā
R
a,b,c\in\mathbb R
a
,
b
,
c
ā
R
:
p
(
a
b
,
c
2
+
1
)
+
p
(
b
c
,
a
2
+
1
)
+
p
(
c
a
,
b
2
+
1
)
=
0
p(ab,c^2+1)+p(bc,a^2+1)+p(ca,b^2+1)=0
p
(
ab
,
c
2
+
1
)
+
p
(
b
c
,
a
2
+
1
)
+
p
(
c
a
,
b
2
+
1
)
=
0
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