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2013 IMO Shortlist
A6
A6
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2013 IMO Shortlist
Problems
(1)
IMO Shortlist 2013, Algebra 6
Source: IMO Shortlist 2013, Algebra 6
7/9/2014
Let
m
≠
0
m \neq 0
m
=
0
be an integer. Find all polynomials
P
(
x
)
P(x)
P
(
x
)
with real coefficients such that
(
x
3
−
m
x
2
+
1
)
P
(
x
+
1
)
+
(
x
3
+
m
x
2
+
1
)
P
(
x
−
1
)
=
2
(
x
3
−
m
x
+
1
)
P
(
x
)
(x^3 - mx^2 +1 ) P(x+1) + (x^3+mx^2+1) P(x-1) =2(x^3 - mx +1 ) P(x)
(
x
3
−
m
x
2
+
1
)
P
(
x
+
1
)
+
(
x
3
+
m
x
2
+
1
)
P
(
x
−
1
)
=
2
(
x
3
−
m
x
+
1
)
P
(
x
)
for all real number
x
x
x
.
algebra
polynomial
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