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Spain Mathematical Olympiad
2007 Spain Mathematical Olympiad
Problem 5
Problem 5
Part of
2007 Spain Mathematical Olympiad
Problems
(1)
Spain Mathematical Olympiad 2007, Problem 5
Source: 2007 Spain Mathematical Olympiad
6/15/2017
Let
a
≠
1
a \neq 1
a
=
1
and be a real positive number and
n
n
n
be an integer greater than
1.
1.
1.
Demonstrate that
n
2
<
(
a
n
+
a
−
n
−
2
)
(
a
+
a
−
1
−
2
)
.
n^2 < \frac{(a^n + a^{-n} -2)}{(a + a^{-1} -2)}.
n
2
<
(
a
+
a
−
1
−
2
)
(
a
n
+
a
−
n
−
2
)
.
algebra
number theory