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Honduran Mathematical Olympiad
2021 Honduras National Mathematical Olympiad
Problem 3
Problem 3
Part of
2021 Honduras National Mathematical Olympiad
Problems
(1)
Honduran National MO (OHM) Intermediate Problem 3
Source: 2021 OHM Intermediate P3
11/21/2021
Let
a
a
a
and
b
b
b
be positive integers satisfying
a
a
−
2
=
b
+
2021
b
+
2008
\frac a{a-2} = \frac{b+2021}{b+2008}
a
−
2
a
=
b
+
2008
b
+
2021
Find the maximum value
a
b
\dfrac ab
b
a
can attain.
algebra
number theory