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Baltic Way
1994 Baltic Way
5
5
Part of
1994 Baltic Way
Problems
(1)
p(x)=1 and p(x)=3 have integer solutions, can p(x)=2 have 2?
Source: Baltic Way 1994
12/22/2011
Let
p
(
x
)
p(x)
p
(
x
)
be a polynomial with integer coefficients such that both equations
p
(
x
)
=
1
p(x)=1
p
(
x
)
=
1
and
p
(
x
)
=
3
p(x)=3
p
(
x
)
=
3
have integer solutions. Can the equation
p
(
x
)
=
2
p(x)=2
p
(
x
)
=
2
have two different integer solutions?
algebra
polynomial
algebra proposed