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Balkan MO
1994 Balkan MO
2
2
Part of
1994 Balkan MO
Problems
(1)
Prove that the polynomial has at most one zero
Source: Balkan MO 1994, Problem 2
4/25/2006
Let
n
n
n
be an integer. Prove that the polynomial
f
(
x
)
f(x)
f
(
x
)
has at most one zero, where
f
(
x
)
=
x
4
−
1994
x
3
+
(
1993
+
n
)
x
2
−
11
x
+
n
.
f(x) = x^4 - 1994 x^3 + (1993+n)x^2 - 11x + n .
f
(
x
)
=
x
4
−
1994
x
3
+
(
1993
+
n
)
x
2
−
11
x
+
n
.
Greece
algebra
polynomial
calculus
integration
modular arithmetic
algebra proposed