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National and Regional Contests
Turkey Contests
Akdeniz University MO
2011 Akdeniz University MO
1
number theory
number theory
Source:
January 31, 2016
number theory
number theory unsolved
Problem Statement
Let
a
a
a
be a positive number, and we show decimal part of the
a
a
a
with
{
a
}
\left\{a\right\}
{
a
}
.For a positive number
x
x
x
with
2
<
x
<
3
\sqrt 2< x <\sqrt 3
2
<
x
<
3
such that,
{
1
x
}
\left\{\frac{1}{x}\right\}
{
x
1
}
=
{
x
2
}
\left\{x^2\right\}
{
x
2
}
.Find value of the
x
(
x
7
−
21
)
x(x^7-21)
x
(
x
7
−
21
)
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