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Baltic Way
2006 Baltic Way
3
3
Part of
2006 Baltic Way
Problems
(1)
polynomial as sum of 3rd degree
Source: Baltic Way 2006
11/8/2006
Prove that for every polynomial
P
(
x
)
P(x)
P
(
x
)
with real coefficients there exist a positive integer
m
m
m
and polynomials
P
1
(
x
)
,
…
,
P
m
(
x
)
P_{1}(x),\ldots , P_{m}(x)
P
1
(
x
)
,
…
,
P
m
(
x
)
with real coefficients such that
P
(
x
)
=
(
P
1
(
x
)
)
3
+
…
+
(
P
m
(
x
)
)
3
P(x) = (P_{1}(x))^{3}+\ldots +(P_{m}(x))^{3}
P
(
x
)
=
(
P
1
(
x
)
)
3
+
…
+
(
P
m
(
x
)
)
3
algebra
polynomial
algebra unsolved