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2003 Poland - Second Round
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3
Part of
2003 Poland - Second Round
Problems
(1)
Polynomial equation
Source: 54 Polish MO 2003 Second Round - First Day Problem 3
4/21/2018
Let
W
(
x
)
=
x
4
−
3
x
3
+
5
x
2
−
9
x
W(x) = x^4 - 3x^3 + 5x^2 - 9x
W
(
x
)
=
x
4
−
3
x
3
+
5
x
2
−
9
x
be a polynomial. Determine all pairs of different integers
a
a
a
,
b
b
b
satisfying the equation
W
(
a
)
=
W
(
b
)
W(a) = W(b)
W
(
a
)
=
W
(
b
)
.
algebra
polynomial
polynomial equation
Poland