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Iran Contests
Iran Team Selection Test
2009 Iran Team Selection Test
8
Iran TST 2009-Day3-P2
Iran TST 2009-Day3-P2
Source:
May 16, 2009
algebra
polynomial
algebra proposed
Problem Statement
Find all polynomials
P
(
x
,
y
)
P(x,y)
P
(
x
,
y
)
such that for all reals
x
x
x
and
y
y
y
,
P
(
x
2
,
y
2
)
=
P
(
(
x
+
y
)
2
2
,
(
x
−
y
)
2
2
)
.
P(x^{2},y^{2}) =P\left(\frac {(x + y)^{2}}{2},\frac {(x - y)^{2}}{2}\right).
P
(
x
2
,
y
2
)
=
P
(
2
(
x
+
y
)
2
,
2
(
x
−
y
)
2
)
.
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