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South East Mathematical Olympiad
2022 South East Mathematical Olympiad
7
no integers on the interval
no integers on the interval
Source: 2022 China Southeast Grade 10 P7
August 3, 2022
number theory
Problem Statement
Let
a
,
b
a,b
a
,
b
be positive integers.Prove that there are no positive integers on the interval
[
b
2
a
2
+
a
b
,
b
2
a
2
+
a
b
−
1
)
\bigg[\frac{b^2}{a^2+ab},\frac{b^2}{a^2+ab-1}\bigg)
[
a
2
+
ab
b
2
,
a
2
+
ab
−
1
b
2
)
.
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