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Kosovo MO 2010 Grade 12, Problem 1
Kosovo MO 2010 Grade 12, Problem 1
Source: Kosovo MO 2010 Grade 12, Problem 1
June 7, 2021
function
algebra
Problem Statement
If the real function
f
(
x
)
=
cos
x
+
∑
i
=
1
n
cos
(
a
i
x
)
f(x)=\cos x+\sum_{i=1}^{n}\cos(a_ix)
f
(
x
)
=
cos
x
+
∑
i
=
1
n
cos
(
a
i
x
)
is periodic, prove that
a
i
,
i
∈
{
1
,
2
,
.
.
.
,
n
}
a_i,i\in\{1,2,...,n\}
a
i
,
i
∈
{
1
,
2
,
...
,
n
}
, are rational numbers.
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