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USAMO
1974
Problem - 3455
Let
a
,
b
,
and
c
denote three distinct integers, and let
P
denote a polynomial having integer coefficients. Show that it is impossible that
P
(
a
)
=
b
,
P
(
b
)
=
c
,
and
P
(
c
)
=
a
.
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