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National and Regional Contests
Chile Contests
Chile National Olympiad
1995 Chile National Olympiad
3
3
Part of
1995 Chile National Olympiad
Problems
(1)
p(a)=b, p(b)=c, p(c)=a not possible for integer cubic (1995 Chile NMO P3)
Source:
11/22/2021
If
p
(
x
)
=
c
0
+
c
1
x
+
c
2
x
2
+
c
3
x
3
p (x) = c_0 + c_1x + c_2x^2 + c_3x^3
p
(
x
)
=
c
0
+
c
1
x
+
c
2
x
2
+
c
3
x
3
is a polynomial with integer coefficients with
a
,
b
,
c
a, b,c
a
,
b
,
c
integers and different from each other, prove that it cannot happen simultaneously that
p
(
a
)
=
b
p (a) = b
p
(
a
)
=
b
,
p
(
b
)
=
c
p (b) = c
p
(
b
)
=
c
and
p
(
c
)
=
a
p (c) = a
p
(
c
)
=
a
.
algebra
polynomial
Cubic