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Saint Petersburg Mathematical Olympiad
2009 Saint Petersburg Mathematical Olympiad
1
Sets of values.
Sets of values.
Source: St Petersburg Olympiad 2009, Grade 11, P1
August 30, 2017
algebra
Problem Statement
f
(
x
)
=
a
x
2
+
b
x
+
c
;
a
,
b
,
c
f(x)=ax^2+bx+c;a,b,c
f
(
x
)
=
a
x
2
+
b
x
+
c
;
a
,
b
,
c
are reals.
M
=
{
f
(
2
n
)
∣
n
is integer
}
,
N
=
{
f
(
2
n
+
1
)
∣
n
is integer
}
M=\{f(2n)|n \text{ is integer}\},N=\{f(2n+1)|n \text{ is integer}\}
M
=
{
f
(
2
n
)
∣
n
is integer
}
,
N
=
{
f
(
2
n
+
1
)
∣
n
is integer
}
Prove that
M
=
N
M=N
M
=
N
or M \cap N = \O
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