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Polish MO Finals
1979 Polish MO Finals
4
4
Part of
1979 Polish MO Finals
Problems
(1)
x_m / y_m <= B x_n / y_n
Source: Polish MO Finals 1979 p4
8/24/2024
Let
A
>
1
A > 1
A
>
1
and
B
>
1
B > 1
B
>
1
be real numbers and (xn) be a sequence of numbers in the interval
[
1
,
A
B
]
[1,AB]
[
1
,
A
B
]
. Prove that there exists a sequence
(
y
n
)
(y_n)
(
y
n
)
of numbers in the interval
[
1
,
A
]
[1,A]
[
1
,
A
]
such that
x
m
x
n
≤
B
y
m
y
n
f
o
r
a
l
l
m
,
n
=
1
,
2
,
.
.
.
\frac{x_m}{x_n}\le B\frac{y_m}{y_n} \,\,\, for \,\,\, all \,\,\, m,n = 1,2,...
x
n
x
m
≤
B
y
n
y
m
f
or
a
ll
m
,
n
=
1
,
2
,
...
algebra
inequalities