MathDB
Problems
Contests
National and Regional Contests
Taiwan Contests
Taiwan APMO Prelininary
2018 Taiwan APMO Preliminary
3
Positive integer solution
Positive integer solution
Source: 2018 Taiwan APMO preliminary
November 10, 2020
algebra
Problem Statement
Let
a
,
b
a,b
a
,
b
be positive integers satisfying
a
b
2
b
2
−
a
=
a
+
2
b
4
b
\sqrt{\dfrac{ab}{2b^2-a}}=\dfrac{a+2b}{4b}
2
b
2
−
a
ab
=
4
b
a
+
2
b
. Find
∣
10
(
a
−
5
)
(
b
−
15
)
∣
+
8
|10(a-5)(b-15)|+8
∣10
(
a
−
5
)
(
b
−
15
)
∣
+
8
.
Back to Problems
View on AoPS