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2019 NMTC Junior
2
There exists an integer
There exists an integer
Source: NMTC 2019 Junior P2
November 2, 2019
number theory
Problem Statement
Given positive real numbers
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
such that
c
d
=
1
cd=1
c
d
=
1
. Prove that there exists at least one positive integer
m
m
m
such that
a
b
≤
m
2
≤
(
a
+
c
)
(
b
+
d
)
.
ab\le m^2\le (a+c) (b+d).
ab
≤
m
2
≤
(
a
+
c
)
(
b
+
d
)
.
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