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Contests
National and Regional Contests
India Contests
India National Olympiad
1999 India National Olympiad
3
3
Part of
1999 India National Olympiad
Problems
(1)
One one polynomials
Source: INMO 1999 Problem 3
10/7/2005
Show that there do not exist polynomials
p
(
x
)
p(x)
p
(
x
)
and
q
(
x
)
q(x)
q
(
x
)
each having integer coefficients and of degree greater than or equal to 1 such that
p
(
x
)
q
(
x
)
=
x
5
+
2
x
+
1.
p(x)q(x) = x^5 +2x +1 .
p
(
x
)
q
(
x
)
=
x
5
+
2
x
+
1.
algebra
polynomial
calculus
integration
quadratics
number theory
algebra unsolved